Study empty polar varieties' impact on singular function-germs.
problem Topology of singular function-germs with nonisolated singularities.
method Analysis of empty polar varieties.
result Topology implications of nonempty polar varieties.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,181 papers · 148 categories
Trend · papers per month
48 results for “singular variety”
Proves Yau-Tian-Donaldson conjecture for certain singular Fano varieties.
problem Proving the conjecture for a specific class of singular Fano varieties.
method Using log smooth resolutions and K-polystability criteria.
result Kähler-Einstein metrics exist for K-polystable singular Fano varieties.
Classifies singularities in quiver varieties for specific Dynkin quivers.
problem Classifying singularities in quiver varieties.
method Classifies singularities using minimal imaginary roots and extended Dynkin quivers.
result Constructs hyper-Kähler cobordisms between binary polyhedral spaces.
Unique tangent cones found for Kahler-Einstein metrics on singular varieties.
problem Finding unique tangent cones for Kahler-Einstein metrics on singular varieties.
method Analyzing unique Ricci flat currents with local bounded potential.
result Local tangent cones of the unique Kahler-Einstein metric are unique.
The paper proves the existence of singular cscK metrics on smoothable varieties.
problem Existence of singular cscK metrics on smoothable varieties.
method Developing a strong topology of pluripotential theory in families and uniform estimates for cscK metrics.
result Existence of singular cscK metrics on -Gorenstein smoothable klt varieties when the Mabuchi functional is coercive.
Study Kähler-Einstein metrics on singular varieties, proving metric completion properties.
problem Kähler-Einstein metrics on singular projective varieties.
method Approximation with constant scalar curvature metrics, RCD space analysis.
result Metric completion of smooth part is non-collapsed RCD space and homeomorphic to original variety.
Proves orbifold singularities for Ricci-flat metrics on certain Kähler varieties.
problem Regularity of singular Ricci-flat Kähler metrics on Kähler varieties with log terminal singularities.
method Analyzes orbifold singularities of metrics restricted to the orbifold locus.
result Singular Ricci-flat Kähler metrics on Kähler varieties with log terminal singularities have orbifold singularities.
The paper extends deformation theory to Calabi-Yau varieties with isolated log canonical singularities.
problem Deformation theory of Calabi-Yau varieties with log canonical singularities.
method Study of higher Du Bois and rational singularities, focusing on 0-liminal singularities.
result Existence of first order smoothings for isolated 0-liminal hypersurface singularities.
Compact RCD spaces derived from singular Kahler metrics on 3D projective varieties.
problem Understanding geometric structures of singular Kahler spaces.
method Proving RCD spaces homeomorphic to 3D projective varieties with bounded Nash entropy and Ricci curvature.
result Compact RCD spaces are equivalent to underlying projective varieties.
Study two types of singular Kähler-Einstein metrics on complex varieties.
problem Understanding different types of singular Kähler-Einstein metrics.
method Analyzing Ricci flat Kähler cone metrics and applying to more general spaces.
result A weaker notion of singular Kähler-Einstein metrics is equivalent to a stronger one under certain conditions.
Study on weighted cscK metrics on Kähler varieties with singularities.
problem Existence of singular weighted cscK metrics on Kähler varieties.
method Resolution of singularities, coercive weighted Mabuchi functional, construction of examples.
result Existence of singular weighted cscK metrics when the weighted Mabuchi functional is coercive.
Proof of complex geometry theorem for specific singular spaces.
problem Proving a complex geometry theorem for a specific type of singular spaces.
method Self-contained proof of singular Beauville-Bogomolov decomposition theorem.
result Proof of singular Beauville-Bogomolov decomposition theorem for compact Kähler varieties with log terminal singularities and zero first Chern class.
Indices of vector fields and 1-forms studied for singular varieties and actions.
problem Understanding indices of vector fields and 1-forms in various contexts.
method Generalization to singular varieties and actions of finite groups.
result New insights into indices of vector fields and 1-forms.
Complex Cayley Grassmannian is a singular variety with smooth singular locus.
problem Characterize the singularities of the Cayley Grassmannian.
method Defined a torus action and used it to prove singularity and cohomology properties.
result Singular locus is smooth and has the same cohomology as .
The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.
problem Extending the Poincaré-Hopf theorem to projective varieties with isolated singularities.
method Using generalized Poincaré-Hopf indices for a projective variety with isolated determinantal singularities.
result A Poincaré-Hopf type theorem is proven for projective varieties with isolated singularities.
Uniformizes varieties with log-canonical singularities using ball quotients.
problem Uniformizing complex projective varieties with log-canonical singularities.
method Criteria based on Miyaoka-Yau inequality and log-resolutions of singularities.
result Criteria for isomorphism to Baily-Borel-Mok compactifications.
The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.
problem Extending the Poincaré-Hopf theorem to varieties with isolated singularities.
method Using generalizations of the Poincaré-Hopf index.
result A Poincaré-Hopf type theorem for projective varieties with isolated singularities.
It is given the diffeomorphism classification on generic singularities of tangent varieties to curves with arbitrary codimension in a projective space. The generic classifications are performed in terms of certain geometric structures and differential systems on flag manifolds, via several techniques in differentiable …
Extends results on smoothability of singular Fano and Calabi-Yau varieties.
problem Smoothability of singular Fano and Calabi-Yau varieties under terminal singularities.
method Generalizes deformation theory results for Calabi-Yau and Fano threefolds to higher dimensions, using higher Du Bois and rational singularities.
result Identifies a class of singularities for which smoothing results hold, including generalized Fano and Calabi-Yau varieties.
The paper studies how the singularity of character varieties changes when representations are extended.
problem Understanding the singularity of character varieties for extended representations.
method Analyzes the variety of characters of fundamental groups in different matrix groups.
result Character varieties become singular when irreducible representations are extended, and the singularity is described.
Generalizes Toledo invariant to singular klt varieties, proving Milnor-Wood inequality.
problem Proving Milnor-Wood inequality for singular klt varieties.
method Generalized Toledo invariant to singular klt varieties and proved Milnor-Wood inequality.
result Milnor-Wood inequality for singular klt varieties.
In this note we discuss the problem of resolving conically singular cscK varieties to construct smooth cscK manifolds, showing a glueing result for (some) crepant resolutions of cscK varieties with discrete automorphism groups.
In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective variety by a reductive algebraic group. Then, by applying the theory of Variation of Geometric Invariant Theory Quotients ([3]), we show tha…
Study of symplectic manifolds degenerating into singular spaces.
problem Understanding degenerations of symplectic manifolds into singular spaces.
method Topological framework focusing on Lagrangian manifolds and holomorphic membranes.
result Degenerations into singular toric varieties yield exotic Lagrangian tori.
Study projective KLT varieties with projectively flat cotangent sheaves.
problem Uniformisation problems on projective varieties with klt singularities.
method Generalising Jahnke-Radloff's work, study torus quotients and varieties with semistable cotangent sheaves and extremal Chern classes.
result Torus quotients are the only klt varieties with semistable cotangent sheaves and extremal Chern classes.
Describes spectral data for singular fibres of a specific Hitchin system.
problem Characterizing singular fibres of the -Hitchin system.
method Using Hecke transformations and analysis of parameter spaces, the paper stratifies and compactifies the singular spaces.
result Large classes of singular fibres are shown to be fibre bundles over Prym varieties.
Establishes K"ahler-Ricci flow on log canonical varieties.
problem Existence and convergence of K"ahler-Ricci flow on varieties with log canonical singularities.
method Generalizes previous results for klt singularities, proves convergence, and constructs solutions with flips.
result Existence and convergence of K"ahler-Ricci flow on semi-log canonical models.
The Miyaoka-Yau inequality for singular varieties with big canonical or anticanonical divisorsmath.AG
The Miyaoka-Yau inequality is proven for certain singular varieties with big canonical or anticanonical divisors.
problem Establishing the Miyaoka-Yau inequality for singular varieties with specific divisors.
method Defining the non-pluripolar product and establishing the Bogomolov-Gieseker type inequality for Higgs sheaves; investigating second Chern class inequalities.
result Proven the Miyaoka-Yau inequality for projective klt varieties with big canonical or anticanonical divisors.
Paper studies curvature properties of singular varieties.
problem Understanding curvature of singular varieties of bounded mean curvature.
method Investigates second-order properties, extends Coarea formula, defines second fundamental form.
result Proves sufficient conditions for area-blow-up set to be empty.
For a G-invariant holomorphic 1-form with an isolated singular point on a germ of a complex-analytic G-variety with an isolated singular point (G is a finite group) one has notions of the equivariant homological index and of the (reduced) equivariant radial index as elements of the ring of complex representations of th…
The study of projective varieties with nef anticanonical divisors and log terminal singularities.
problem Understanding the structure and properties of projective varieties with specific divisor conditions.
method Analyzing the Albanese map and MRC fibration for klt projective varieties, showing locally constant fibrations and product decompositions.
result Generalization of results for smooth projective varieties to the klt case, including decomposition into rationally connected and projective varieties with trivial canonical divisor.
Proves certain Calabi-Yau varieties are projective.
problem Compact Calabi-Yau varieties with isolated singularities are not always projective.
method Analysis and Ohsawa's degenerate spectral sequence in higher dimensions.
result Proves compact Calabi-Yau varieties with certain isolated singularities are projective.
Existence of metrics on non-Kähler varieties, generalizing previous work.
problem Existence of metrics on non-Kähler varieties.
method Definition of slope stability and existence of singular Hermite-Einstein metrics.
result Existence and uniqueness of singular Hermite-Einstein metrics for slope-stable sheaves.
Proves Kähler-Ricci shrinkers are complex analytic varieties.
problem Characterizing singular Kähler-Ricci shrinkers.
method Analyzes limits of Kähler-Ricci flows and applies algebraic geometry.
result Singular Kähler-Ricci shrinkers are locally algebraic complex-analytic varieties.
By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric quantization) is the projective coordinate ring of the embedded manifold. This all…
Study Kähler-Einstein potentials on stable varieties near singularities
problem Asymptotic behavior of Kähler-Einstein potentials on stable varieties near singularities
method Using iterated logarithmic functions and refined lower bounds
result Improved estimates for Kähler-Einstein potentials
Abstract: Study of metrics on line bundles over complex varieties.
problem Chern-Weil and Hilbert-Samuel formulae for singular metrics.
method Theory of b-divisors and multiplier ideal volume function.
result Generalization of a result for elliptic curves to higher degrees.
Explains complex analytic invariants of vector fields and foliations.
problem Integrating theories of singular varieties and foliations.
method Expository discussion of invariants.
result Introduces connections between complex analytic singular varieties and foliations.
Uniform K-stability implies Kähler-Einstein metric for Q-Fano varieties.
problem Proving the existence of Kähler-Einstein metrics for uniformly K-stable singular Fano varieties.
method Modified Berman-Boucksom-Jonsson's strategy with perturbative arguments and non-Archimedean estimates.
result Uniform K-stability is equivalent to the existence of Kähler-Einstein metrics for Q-Fano varieties.
Generalizes nonabelian Hodge theory to klt singularities.
problem Applying nonabelian Hodge theory to spaces with klt singularities.
method Uses descent theorems for numerically flat vector bundles and a new restriction theorem for semistable Higgs sheaves.
result Establishes a new restriction theorem for semistable Higgs sheaves.
Uniform bounds prove connection between Kähler metrics and RCD spaces.
problem Bounding Nash entropy and Calabi energy for Kähler metrics.
method Proving uniform Sobolev bounds for Kähler manifolds.
result Establishes connection to RCD spaces and provides examples.
Study calculates instanton homology for simple braids, linking to Fano variety quantum cohomology.
problem Calculating instanton homology for specific braids.
method Using local coefficients and algebraic curves, calculates homology groups and their module structures.
result Equivalent to computing quantum cohomology of a moduli space of parabolic bundles.
Calabi-Yau coverings over some singular varieties and new Calabi-Yau 3-folds with Picard number onemath.AG
This note is a report on the observation that some singular varieties admit Calabi--Yau coverings. As an application, we construct 18 new Calabi--Yau 3-folds with Picard number one that have some interesting properties.
Reductive quotients preserve klt singularities in algebraic geometry.
problem Preserving klt singularities in quotients of klt singularities.
method Proving that the quotient of a klt type singularity by a reductive group is of klt type.
result The quotient of a klt variety by a reductive group results in a klt variety with a suitable boundary.
Continuity of Kähler-Einstein potentials at singularities proven.
problem Regularity of solutions to degenerate complex Monge-Ampère equations on singular spaces.
method Investigation of Dirichlet problem and global continuity of solutions.
result Kähler-Einstein potentials are continuous at isolated singularities.
In this paper we define the adjoint Reidemeister torsion as a differential form on the character variety of a compact oriented 3-manifold with toral boundary, and prove it defines a regular volume form. Then we show that the torsion form can vanish only at singular points of the character variety. In fact, if the singu…
The paper classifies certain singular projective varieties with specific properties.
problem Classifying projective klt pairs with nef anti-log canonical divisors.
method Establishes a structure theorem using locally trivial rationally connected fibrations.
result Projective klt pairs can be decomposed into rationally connected and Calabi-Yau varieties.
Constructs Morse homology for complex algebraic varieties.
problem Homology of vanishing cycles in complex algebraic varieties.
method Morse homology groups associated with a perturbed function on a compactified variety.
result Morse homology groups are isomorphic to the homology of vanishing cycles.