180 papers
This paper advances the theory of holonomic D-modules by establishing the invariance of Euler characteristics under localization and regular singular twists, proving local generic vanishing theorems via twisting with differential forms, and providing a direct construction of the Laplace transform for Stokes-filtered sheaves that completes the correspondence with holonomic D-modules.
This paper investigates the geometry of compact Kähler manifolds with partially semi-positive curvature by proving that such manifolds are rationally connected under specific positivity conditions and establishing structure theorems that classify them as either having high rational dimension or admitting a locally constant fibration with rationally connected fibers and a Ricci-flat base.
This paper establishes that the tropical rank of a semimodule of tropical rational functions equals its topological dimension, while demonstrating that verifying tropical independence is equivalent to solving a turn-based stochastic mean-payoff game and that computing the tropical rank is NP-hard.
This paper classifies intermediate t-structures on the local derived category of a 3-fold flopping contraction and minimal resolutions of Kleinian singularities, thereby describing the complete lattice of torsion classes for associated modification and preprojective algebras and providing foundational steps for understanding spherical objects in derived categories of surfaces and 3-folds.
This paper determines the unique birationally rigid induction datum for every -equivariant nilpotent cover of a nilpotent coadjoint orbit in a semisimple simply connected algebraic group of exceptional type over .
This paper generalizes the construction of mixed Hodge module structures to tautological systems associated with homogeneous spaces via a functorial approach, thereby providing a complete solution to the holonomic rank problem for these systems.
This paper demonstrates that twisted sectors in the vanishing cohomology of one-parameter deformations of Calabi-Yau type Fermat polynomial singularities, along with the genus zero Gromov-Witten generating series of the corresponding varieties, are components of automorphic forms for certain triangular groups, utilizing mixed Hodge structures, the Riemann-Hilbert correspondence, and genus zero mirror symmetry.
This paper presents explicit examples of K3 surfaces over with geometric Picard rank 1, specifically constructing degree 10 surfaces as intersections of hyperplanes, a quadric, and the Grassmannian in , as well as a degree 6 example.
This paper establishes simple left-inverse characterizations of the singularity invariants , , and for equidimensional varieties and utilizes a trace morphism to prove their descent under finite surjective morphisms.
This paper demonstrates that in o-minimal structures, every definable mapping that is Lipschitz with respect to the inner metric can be approximated by (or if the structure admits smooth cell decomposition) mappings with arbitrarily close derivative bounds, a result achieved through the construction of partitions of unity with sharp derivative estimates and extended to outer Lipschitz mappings.
This paper classifies flexible Kokotsakis polyhedra with non-planar quadrilateral faces by analyzing the conditions under which the polynomials relating their dihedral angles are reducible, thereby characterizing the specific shape restrictions that enable flexibility.
This paper employs tropical geometry and Hamiltonian flows to derive explicit formulae for leaky Hurwitz numbers in genus 0 and prove that these invariants satisfy topological recursion under fixed leakiness, thereby establishing a partial inverse to recent results on KP -functions.
This paper presents an explicit counterexample demonstrating that the natural map from a smooth projective variety to its Campana orbifold base is not necessarily an orbifold morphism, while also establishing conditions under which this property holds and discussing the implications for Campana's conjectures regarding dense entire curves and integral points.
This paper establishes an explicit characterization of irregular Hodge numbers for twisted de Rham cohomology groups in terms of classical Hodge numbers, demonstrating their independence from the choice of non-degenerate functions and providing a concrete formula for unipotent non-degenerate cases.
This paper proves Oort's conjecture that the automorphism group of a generic principally polarized supersingular abelian variety in characteristic is , except for the specific cases of genus 2 or 3 with , while also providing an explicit description of the -locus in the corresponding Rapoport-Zink space and establishing analogous results for supersingular -divisible groups.
Motivated by non-abelian Hodge theory, this paper formulates a Hodge-theoretic version of Grothendieck's anabelian conjecture by replacing Galois actions with natural -actions, proving an analog of Mochizuki's theorem for smooth projective hyperbolic curves over and extending the result to higher-dimensional ball quotient manifolds.
This paper proves that augmented admissible sets in Iwahori-Weyl groups are dual EL-shellable, thereby resolving a conjecture of Görtz and establishing the Cohen-Macaulayness of special fibers for local models with parahoric level structure—including previously open cases in residue characteristic 2 and non-reduced root systems—through a characteristic-free, intrinsic construction that yields an explicit shelling and inductive building procedure.
This paper constructs a presheaf of Koszul complexes on weighted finite subsets of Euclidean space, utilizing linearized coefficients and change-of-coordinates maps to form a Čech-Koszul bicomplex whose degree-0 cocycles capture homotopical relationships between locally defined least squares solutions on data overlaps.
This paper computes Donaldson-Thomas invariants and their descendants for the local Calabi-Yau 4-fold over the Mukai-Umemura variety using localization formulas, thereby verifying the predictions of Cao, Maulik, and Toda under the assumption that genus-one Gopakumar-Vafa invariants vanish.
This paper constructs and analyzes the birational geometry of a Kausz-type compactification of the space of symmetric matrices by realizing it as an evaluation fiber in the Kontsevich space of pointed conics on the Lagrangian Grassmannian, while also presenting analogous results for orthogonal Grassmannians.