The paper explores Newton-Cartan structures with torsion on Kodaira moduli spaces.
problem Understanding Newton-Cartan spacetimes and their deformations.
method Construction of connections and frames on Kodaira moduli spaces, generalizing canonical connections to include torsion.
result Novel twistor theories of Newton-Cartan spacetimes in three and five dimensions, including torsion.
New findings on Frobenius structures on Kodaira manifolds.
problem Understanding Frobenius structures on Kodaira manifolds.
method Extended deformation theory and Frobenius structures.
result Frobenius structure on Kodaira manifolds is trivial on degree-2 component.
Study topological hyperbolicity of moduli spaces of elliptic surfaces.
problem Characterize the largeness of the topological fundamental group of complex varieties.
method Introduce topological hyperbolicity and provide supporting evidence for moduli spaces of elliptic surfaces.
result Establish a weak form of topological hyperbolicity for moduli spaces of elliptic surfaces of Kodaira dimension one.
Study examines geometry of moduli space with bundle jumps and hypercomplex structures.
problem Investigates the geometry of Kodaira moduli space with bundle jumps.
method Identifies natural assumptions for extending Obata connection to logarithmic connection.
result Natural assumptions guarantee extension of Obata connection to logarithmic connection.
Researchers create a projective space for quasimaps and study its connections to Calabi-Yau fibrations.
problem Understanding the moduli spaces of quasimaps and Calabi-Yau fibrations.
method Constructing a projective K-moduli space of quasimaps and investigating relationships with Calabi-Yau fibrations.
result Entire quasi-projectivity and ampleness of the CM line bundle on the normalization of the K-moduli space of Calabi-Yau fibrations.
There is a natural sequence of CY manifolds that are double covers of the projective g dimensional spaces ramified over 2g+2 hyperplanes. We observe that some of them are obtained as quotient of the action of the semi-direct product of g-1 copies of cyclic Z/2Z groups with the symmetric g group on the product of g-copi…
A general theorem on the existence of natural torsion-free affine connections on a complete family of compact complex submanifolds in a complex manifold is proved. Applications to twistor theory are discussed.
This thesis was motivated by a desire to understand the natural geometry of hyperbolic monopole moduli spaces. We take two approaches. Firstly we develop the twistor theory of singular hyperbolic monopoles and use it to study the geometry of their charge 1 moduli spaces. After this we introduce a new way to study the m…
Study on Kodaira fibrations with nontrivial cohomology, proving properties of their structure.
problem Characterizing Kodaira fibrations with specific cohomology properties.
method Analyzing invariant rational cohomology and properties of holomorphic sections.
result Kodaira fibrations with invariant cohomology admit specific coverings and monodromies.
It is conjectured that the moduli b-divisor of the Kawamata-Kodaira canonical bundle formula associated to a klt-trivial fibration (X,B)→Z is semi-ample. In this paper, we show the semi-ampleness of an arbitrarily small perturbation of the moduli b-divisor by a fixed appropriate divisor which roughly speaking come…
Stability defined for maps between polarised varieties in higher dimensions.
problem Defining stability for maps between polarised varieties in higher dimensions.
method Formulated a notion of stability generalizing existing definitions.
result Existence of a projective moduli space of canonically polarised stable maps.
Study on positivity of CM line bundles on moduli space of klt good minimal models with κ=1.
problem Positivity of CM line bundles on moduli space of klt good minimal models with κ=1.
method Construction of a moduli space of numerical equivalence classes, proving projectivity of moduli space of ε-stable quotients, and using K-moduli of quasimaps.
result CM line bundle becomes ample after normalization and moduli space is quasi-projective.
Study finite deformations from heterotic superpotential, leading to new complex effective action.
problem Finite deformations of the Hull--Strominger system.
method Expanding the heterotic superpotential around a supersymmetric vacuum, identifying complex coordinates, and using Maurer--Cartan equation.
result Generalizes complex effective action of Kodaira--Spencer and holomorphic Chern--Simons theory, with a supersymmetric locus described by an L3 algebra. Holomorphic supergravity theory simplifies anomaly cancellation in heterotic moduli.
problem Anomaly cancellation in heterotic moduli space.
method Formulated a ten-dimensional version of Kodaira-Spencer gravity, quantized fluctuations, and showed partition function simplification.
result Holomorphic supergravity theory simplifies anomaly cancellation and relates to type I Kodaira-Spencer theory.
The main goal of this work is to construct and study a reasonable compactification of the strata of the moduli space of Abelian differentials. This allows us to compute the Kodaira dimension of some strata of the moduli space of Abelian differentials. The main ingredients to study the compactifications of the strata ar…
New groups without finite classifying spaces found in Kodaira fibrations.
problem Finding groups without finite classifying spaces.
method Constructing Kähler groups as fundamental groups of Kodaira fibrations.
result Found Kähler groups that are not commensurable to surface groups and do not have finite classifying spaces.
For any integer k we construct an explicit example of a twistor space which contains a one--parameter family of jumping rational curves, where the normal bundle changes from O(1)+O(1) to O(k)+O(2−k). For k>3 the resulting anti--self--dual Ricci-flat manifold is a Zariski cone in the space of holomorphic section…
New theory connects string theory to swampland distance conjecture.
problem Connecting string theory to swampland distance conjecture.
method Deformations of the heterotic superpotential, treating separately for large fluxes or large distances, integrating out fields to obtain a new field theory.
result New holomorphic theory defined, connects to swampland distance conjecture.
Computational techniques calculate dimensions of complex structures.
problem Calculating dimensions of complex structures on manifolds.
method Developed computational techniques to calculate Kodaira dimension and Dolbeault harmonic forms.
result Computed dimensions of left-invariant almost complex structures.
Study on constant mean curvature 1-immersions into hyperbolic 3-manifolds.
problem Understanding CMC 1-immersions of surfaces into hyperbolic 3-manifolds.
method Parametrization of moduli space, analysis of blow-up phenomena, asymptotic analysis.
result Sharp condition for genus g=2 involving Kodaira map at six Weierstrass points.
We define analogue of theta-functions on the Kodaira--Thurston manifold which is a compact 4-dimensional symplectic manifold and use them to construct canonical symplectic embedding of the Kodaira--Thurston manifold into the complex projective space (analogue of the Lefshetz theorem).
We bound the index of a subgroup in iterated Kodaira fibrations.
problem Bounding the index of a subgroup in iterated Kodaira fibrations.
method Passing to a finite index subgroup of π_1(X) to achieve the desired structure.
result We provide a bound on the index of such a group.
The paper explores curvature constraints on Kodaira dimension for specific almost Hermitian manifolds.
problem Investigating Riemannian curvature constraints on the Kodaira dimension of compact almost Hermitian manifolds.
method Analyzing compact almost Hermitian manifolds in the Gray-Hervella class and Hermitian manifolds with nonnegative scalar curvature.
result For compact almost Hermitian manifolds with nonnegative scalar curvature, the Kodaira dimension is either -∞ or 0, with specific conditions.
We study a class of asymptotically cylindrical Ricci-flat Kähler metrics arising on quasiprojective manifolds. Using the Calabi--Yau geometry and analysis and the Kodaira--Kuranishi--Spencer theory and building up on results of N.Koiso for the case of compact manifolds, we show that under rather general hypotheses any …
The paper studies Kähler-Einstein metrics on fiber spaces with positive Kodaira dimension.
problem Understanding Kähler-Einstein metrics on fiber spaces with positive Kodaira dimension.
method Analyzes the properties of singular Kähler-Einstein metrics and their curvature.
result The fiberwise singular Kähler-Einstein metric induces a semipositively curved metric on the relative canonical bundle.
This article gives an exposition of the deformation theory for pairs (X,E), where X is a compact complex manifold and E is a holomorphic vector bundle over X, adapting an analytic viewpoint à la Kodaira-Spencer. By introducing and exploiting an auxiliary differential operator, we derive the Maurer--Cartan equa…
The paper examines Kodaira dimensions of specific complex 4-manifolds with torsion first Chern class.
problem Investigating the Kodaira dimension of almost complex 4-manifolds with torsion first Chern class.
method Developed theory of pseudoholomorphic structures on vector bundles, computed tangent spaces of infinitesimal deformations, and proved unobstructedness theorems.
result Proved that Kodaira dimension can only be 0 or -∞ for tamed almost complex structures.
Let M=G/Γ be a compact nilmanifold endowed with an invariant complex structure. We prove that, on an open set of any connected component of the moduli space C(g) of invariant complex structures on M, the Dolbeault cohomology of M is isomorphic to the one of the differential bigraded algebra ass…
Defines and classifies Thurston geometries and connects simplicial volume to Kodaira dimension.
problem Classifying Thurston geometries and understanding their properties.
method Introduces an axiomatic definition for the Kodaira dimension and studies its compatibility with traditional notions.
result Establishes a connection between the simplicial volume and the holomorphic Kodaira dimension, showing implications for smooth Kähler 3-folds.
We embed polarised orbifolds with cyclic stabiliser groups into weighted projective space via a weighted form of Kodaira embedding. Dividing by the (non-reductive) automorphisms of weighted projective space then formally gives a moduli space of orbifolds. We show how to express this as a reductive quotient and so a GIT…
We present the extended Kuranishi space for Kodaira surface as a non-trivial example to Kontsevich and Barannikov's extended deformation theory. We provide a non-trivial example of Hertling-Manin's weak Frobenius manifold. In addition, we find that Kodaira surface is its own mirror image. Our computation is done in the…
Extends Kodaira Spencer to higher-dimensional Calabi-Yau manifolds.
problem No specific problem stated; extension of functional.
method Extension to Calabi-Yau manifolds of arbitrary dimension.
result Extension of the Kodaira Spencer functional.
The Kodaira-Thurston manifold is a quotient of a nilpotent Lie group by a cocompact lattice. We compute the family Gromov-Witten invariants which count pseudoholomorphic tori in the Kodaira-Thurston manifold. For a fixed symplectic form the Gromov-Witten invariant is trivial so we consider the twistor family of left-in…
Study on types of generalized hypercomplex structures on tori and Kodaira-Thurston surface.
problem Characterizing types of generalized hypercomplex structures.
method Analysis of S2-family of generalized complex structures and study of twistor spaces. result Existence of generalized hypercomplex structures on 4n-dimensional tori with non-maximal types. Study on Kodaira dimension of almost Kähler manifolds and their curvature.
problem Understanding Kodaira dimension in almost Kähler manifolds.
method Explicit computation and analysis of curvature of the canonical connection.
result Ricci curvature vanishes for members of the family of almost Kähler manifolds.
Proves Vaisman solvmanifolds are finite quotients of Kodaira-Thurston manifolds.
problem Characterizing Vaisman solvmanifolds and their properties.
method Analyzing fundamental groups and quotient structures.
result Every Vaisman solvmanifold is a finite quotient of a Kodaira-Thurston manifold.
Study on Kodaira dimension of SU(m)-structures on almost complex manifolds.
problem Understanding the Kodaira dimension of almost complex manifolds with SU(m)-structures.
method Introduced almost complex structure of splitting type and associated SU(m)-structure. Provided constructions for non-invariant almost complex structures with specific Kodaira dimensions.
result Found non-invariant almost complex structures with Kodaira dimensions 0 and -∞.
The paper addresses deformations of Kähler spaces with vanishing first Chern class.
problem Deformations of Kähler spaces with specific properties.
method Analyzes locally trivial deformation spaces and uses cohomological vanishing conditions.
result Shows that under certain conditions, deformations of Kähler spaces are projective varieties.
Study Kodaira dimensions on almost complex manifolds, proving integrability and structural descriptions.
problem Understanding Kodaira dimensions on almost complex manifolds.
method Using pseudoholomorphic pluricanonical maps, defining new dimensions, and applying probabilistic combinatorics.
result Almost complex structures with top Kodaira dimension are integrable, and for compact 4-manifolds, they have elliptic fibration structures.
Automorphisms of Kodaira surfaces are shown to be affine transformations.
problem Characterizing automorphisms of Kodaira surfaces.
method Analyzing lifts to the universal cover and conditions on affine transformations.
result Precise description of Kodaira surfaces' automorphism groups.
In this note we show that the Lagrangian Luttinger surgery preserves the symplectic Kodaira dimension. Some constraints on Lagrangian tori in symplectic four manifolds with non-positive Kodaira dimension are also derived.
Study extra-special quotients of surface braid groups and construct double Kodaira fibrations.
problem Investigate non-abelian finite quotients of surface braid groups and double Kodaira fibrations with small signature.
method Introduced diagonal double Kodaira structures to study finite quotients of pure braid groups and constructed double Kodaira fibrations.
result Proved that if a finite group admits a diagonal double Kodaira structure, then its order is at least 32, with equality if and only if the group is extra-special.
Study on surface bundles, CAT(0) groups, and mapping class groups.
problem Properties of surface bundles and their mapping class groups.
method Geometric and group theoretical analysis of surface bundles and their monodromies.
result Constraints on Kodaira fibrations and properties of surface bundles over surfaces.
Study on Vaisman metrics on Kodaira-Thurston surface using pluriclosed flow.
problem Characterizing and preserving Vaisman metrics on Kodaira-Thurston surface.
method Characterization of T2-invariant Vaisman metrics, analysis of pluriclosed flow behavior. result Pluriclosed flow preserves Vaisman condition on Kodaira-Thurston surface, including non-constant scalar curvature.
New curvature condition ensures projectivity of Kähler manifolds.
problem Characterize projectivity of Kähler manifolds using curvature.
method Introduced a new curvature condition and proved it implies projectivity.
result Positive 2nd scalar curvature guarantees projectivity of Kähler manifolds.
Generalizes Kodaira vanishing theorem to Kahler Lie algebroids.
problem Extending complex geometry results to Lie algebroids.
method Using local coordinate calculations to generalize Kahler identities.
result Kernel of Lie algebroid Laplace operator vanishes for sufficiently large p+q.
We define the Kodaira dimension for 3-dimensional manifolds through Thurston's eight geometries, along with a classification in terms of this Kodaira dimension. We show this is compatible with other existing Kodaira dimensions and the partial order defined by non-zero degree maps. For higher dimensions, we explore th…
The paper generalizes a key theorem in complex geometry.
problem Complex geometry theorems and their generalizations.
method Analytical methods
result Generalization of the Kodaira embedding theorem