170 papers
This paper establishes a de Rham and Hyodo-Kato flip-flopping theorem for dual towers of rigid analytic spaces by utilizing pro-étale comparison theorems, and applies this result to prove the admissibility of the de Rham and Hyodo-Kato cohomologies of finite level coverings of Drinfeld spaces as representations of .
This paper develops an explicit invariant calculus for noncommutative linear differential operators using noncommutative Bell polynomials to derive universal formulas for gauge-covariant Wilczynski invariants and their projective counterparts, subsequently globalizing the framework to construct modular and Siegel modular differential operators on Riemann surfaces.
This paper proves the conjectural correspondence between logarithmic Gromov-Witten and Donaldson/Pandharipande-Thomas theories for toric threefold pairs with singular boundaries, while also establishing new results such as the Laurent polynomial nature of capped vertices and verifying the logarithmic DT/PT conjecture.
The paper presents a new characterization of Fano type varieties.
This survey reviews the computation of Weil-Petersson and Masur-Veech volumes for moduli spaces of Riemann surfaces, highlighting their profound impact on combinatorial enumeration, intersection theory, and recursion relations, while drawing parallels between the methods used to calculate these two distinct types of volumes.
This paper establishes a combinatorial sufficient condition based on multinet structures for the Milnor fiber of a complex hyperplane arrangement to be non-1-formal and uses this criterion to construct an infinite family of monomial arrangements with non-formal Milnor fibers.
This paper establishes a comparison between the Segre motivic Chern classes of open projected Richardson varieties and affine Schubert cells via the affine Grassmannian using Demazure–Lusztig operators, while also relating these classes to twisted Kazhdan–Lusztig R-polynomials and providing a combinatorial formula for the Grassmannian case.
This paper establishes a logarithmic Bott localization formula for global holomorphic sections of on a compact complex manifold with a simple normal crossings divisor, extending the theory to non-isolated zero schemes that are local complete intersections and providing a current-theoretic formulation that identifies the local residue with a Coleff-Herrera current.
This paper proves that the Lefschetz filtration and the perverse filtration on the cohomology of the compactified Jacobian of a complex integral curve with planar singularities are opposite to each other, thereby confirming a conjecture by Maulik and Yun.
This paper investigates linear -quotients on affine spaces by employing explicit stacky resolutions to classify their singularity types and compute stringy motivic invariants, thereby reducing a conjecture by the authors and Fabio Tonini—which posits that these invariants match those of linear -quotients—to a computationally verified equality of multi-sets.
The paper proves that equivariantly simple invariant singularities can only exist for real representations and certain "almost real" representations of a group of prime order.
This short note refutes two natural conjectures regarding polynomial count varieties by demonstrating that a smooth variety with a point count of is not necessarily isomorphic to affine space, and that such varieties do not necessarily have vanishing Hodge numbers for .
This paper establishes the equivalence between Bogomolov's instability theorem and the Miyaoka-Sakai theorem on surfaces in positive characteristic, demonstrating how their interplay yields partial vanishing results, new proofs for Kawamata-Viehweg vanishing on del Pezzo surfaces, and Reider-type results for Fujita's conjecture.
This paper generalizes the classical multiplicity of an ideal to graded families of ideals on Noetherian local rings, establishing that many fundamental theorems (such as Rees' theorem and the Minkowski inequality) hold for this new invariant through simple proofs based on intersection products on blow-up schemes, independent of volume theory and Okounkov bodies.
This paper provides a characterization of ball quotients among minimal smooth projective varieties of general type solely in terms of their characteristic numbers, thereby generalizing previous results by Miyaoka, Yau, and Greb–Kebekus–Peternell–Taji.
This paper presents a method for computing the of effective log motives to demonstrate their -invariance and applies these results to establish the full faithfulness of the stripping functor from log motivic sheaves to Nisnevich sheaves with transfers.
This paper investigates the multigraded Betti numbers of Veronese embeddings by interpreting them through Hochster's formula as homology groups of specific simplicial complexes and utilizing Forman's discrete Morse theory to establish vanishing and non-vanishing results.
This paper extends the concepts of higher Du Bois and higher rational singularities to pairs within the minimal model program, proving their stability under finite maps and the implication that m-rational pairs are m-Du Bois via a generalized injectivity theorem.
This paper characterizes isogeny classes of abelian surfaces over finite fields that contain no curves of genus 3 or less by completing the classification for genus up to 2, establishing a link between genus 3 curves and degree 4 polarizations, and describing the specific genus 3 curves that exist on such surfaces.
This paper proves that, under mild assumptions, the Fano surfaces of lines on smooth cubic threefolds are the unique smooth subvarieties of abelian varieties whose Tannaka group for the convolution of perverse sheaves is an exceptional simple group, thereby significantly strengthening previous results on the Shafarevich conjecture.