arXiv research

Study calculates Euler obstruction for determinantal varieties with ICIS singular set.

Study characteristic classes of a specific type of determinantal varieties.

The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.

Study Euler obstruction of 1-forms on determinantal singularities.

The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.

Local models for special Kähler structures in 2D computed without essential singularities.

We prove that there are just two types of isolated singularities of special Kähler metrics in real dimension two provided the associated holomorphic cubic form does not have essential singularities. We also construct examples of such metrics.

We establish a Lehto--Virtanen-type theorem and a rescaling principle for an isolated essential singularity of a holomorphic curve in a complex space, which are useful for establishing a big Picard-type theorem and a big Brody-type one for holomorphic curves.

Extends Frohman and Rannard's result to Seifert fiber spaces with singular surfaces.

New method detects essential tori in mixed singularity links.

Wavelet analysis reveals limitations in detecting multifractality in signals with isolated singularities.

Classifies solutions of Toda equations near singularities.

The study confirms a conjecture about critical points of smooth functions.

Deterministic bounds for tensor singular values and vectors, differing from matrix cases.

Study finds all local models for flat metrics with isolated singularities.

Defines Perelman's functionals on manifolds with non-isolated conical singularities.

Study of $G_2$-structures with isolated singularities and bounded torsion.

Proves conditions for positive scalar curvature on certain manifolds with conical singularities.

New hyperbolic metrics with isolated singularities constructed.

Study reveals GAGA phenomenon in Poisson cohomology for plane structures with isolated singularities.

Study classifies non-removable singularities in Minkowski 3-space equations.

Constructs a Dolbeault-Hilbert complex for spaces with isolated singular points.

We investigate the face numbers of simplicial complexes with Buchsbaum vertex links, especially pseudomanifolds with isolated singularities. This includes deriving Dehn-Sommerville relations for pseudomanifolds with isolated singularities and establishing lower bound theorems when the singularities are also homological…

Constructs Kahler-Einstein metrics near isolated log canonical singularities.

Study shows isolated singularities in maps to K3 surfaces.

Study on solutions near isolated singularities in 6D Yamabe equation.

J. Nitsche's theorem on conformal hyperbolic metrics is extended with new expressions for metrics near isolated singularities.

Proves uniqueness of tangent cones for specific types of connections.

Extends Khimshiashvili's degree formula to non-isolated singularities.

Formula calculates homology groups of Milnor fibres for real hypersurface singularities.

In the present paper, we deform isolated singularities of a certain class of polar weighted homogeneous mixed polynomials, and show that there exists a deformation which has only definite fold singularities and mixed Morse singularities.

The abstract extends a Poincaré-Hopf formula to non-isolated singularities.

The paper extends deformation theory to Calabi-Yau varieties with isolated log canonical singularities.

Study finds solutions to Yamabe equation with specific behavior near singular points.

The paper builds complex hyperbolic 2-manifolds with isolated singularities.

Proves heat expansion for Laplacian on a singularity.

Study links curve singularities to quiver mutations.

We study the local symplectic algebra of the 0-dimensional isolated complete intersection singularities. We use the method of algebraic restrictions to classify these symplectic singularities. We show that there are non-trivial symplectic invariants in this classification.

For isolated complex hypersurface singularities with real defining equation we show the existence of a monodromy vector field such that complex conjugation intertwines the local monodromy diffeomorphism with its inverse. In particular, it follows that the geometric monodromy is the composition of the involution induced…

Study removes singularities from area-minimizing surfaces.

Study shows infinite order in mapping class groups for certain 3D shapes.

Constructs graphs with singularities in a special space.

Given a real analytic function $f$ from $\mathbb{R}^4$ to $\mathbb{R}^2$ with isolated critical point at the origin, the link $L_f$ of the singularity is a real fibred knot in $\mathbb{S}^{3}$. From this singularities, we construct a family of real isolated suspension singularities from $\mathbb{R}^6$ to $\mathbb{R}^2$…

We show that in cohomogeneity 3 there are G-manifolds with any given number of isolated singular orbits and an invariant metric of positive Ricci curvature. We show that the corresponding result is also true in cohomogeneity 5 provided the number of singular orbits is even.

Survey connects singularity invariants to link pairings.

Analytic lattice cohomology defined for isolated singularities, linking to Heegaard Floer cohomology.

New special Lagrangian submanifolds with multiple conical singularities found.

We study graphs of positive extrinsic curvature with a non-removable isolated singularity in 3-dimensional warped product spaces, and describe their behavior at the singularity in several natural situations. We use Monge-Ampère equations to give a classification of the surfaces in 3-dimensional space forms which are em…