2549 papers
This paper introduces the concept of noncommutatively stably semiorthogonally indecomposable (NSSI) varieties, proves that varieties with finite Albanese morphisms and certain fibrations possess this property, and demonstrates that NSSI varieties ensure the indecomposability of their subvarieties' derived categories and the absence of phantom subcategories in specific products like .
This paper establishes an intrinsic version of Thomason's fixed-point theorem to analyze the local structure and singularity types of Hilbert schemes of up to seven points in , ultimately computing equivariant Hilbert functions at singularities to verify Zhou's conjecture on the Euler characteristics of tautological sheaves for up to six points on .
This paper develops a theory of filtered formal groups and their Cartier duality, utilizes a deformation to the normal cone in derived algebraic geometry to establish a unicity result linking adic filtrations to -equivariant degenerations, and applies these findings to recover the filtration on the filtered circle and lift Hochschild homology invariants to spectral algebraic geometry.
This paper presents algorithms grounded in invariant theory to address geometric problems concerning curves and hypersurfaces, with a primary focus on those of genus 2, 3, and 4, while also incorporating new theoretical results derived from the first author's PhD thesis.
This paper demonstrates that over the complex numbers, the infinite Weil divisor associated with any approximable graded algebra necessarily possesses a finite cohomology class.
This paper constructs trace maps for the six functor formalism of motivic cohomology and provides an -enhancement of this formalism by reinterpreting the trace maps functorially using Suslin-Voevodsky's relative cycle groups.
This paper establishes that for classical unramified reductive groups over non-archimedean local fields, specific -adic Deligne–Lusztig spaces associated with basic elements and Coxeter elements decompose into disjoint unions of translates of integral -adic Deligne–Lusztig spaces, while also extending results on rational conjugacy classes of unramified tori and proving a loop version of Frobenius-twisted Steinberg's cross section.
The authors utilize Dolgachev elliptic surfaces to derive explicit equations for two new pairs of fake projective planes with an automorphism group of order 21, including J. Keum's discovery, thereby completing the classification of such explicit equations for this specific automorphism group.
This paper classifies the maximal algebraic subgroups of the group of birational transformations of ruled surfaces over a smooth projective curve of positive genus.
This paper introduces the concept of multi-weighted blow-ups to construct an explicit, functorial algorithm for resolving singularities of reduced closed subschemes in characteristic zero by iteratively blowing up the worst singular locus until the result becomes a simple normal crossing divisor.
This paper demonstrates that when a reductive complex algebraic group acts freely on the stable locus of a complex vector space, the components of the fixed point locus of a torus action on the resulting GIT quotient are themselves GIT quotients of linear subspaces by Levi subgroups.
This paper introduces affine subspace concentration conditions for lattice polytopes and proves their validity for smooth and reflexive polytopes with the origin as their barycenter by analyzing the slope stability of the canonical extension of the tangent bundle on Fano toric varieties.
This paper introduces perverse-Hodge complexes for Lagrangian fibrations and proposes a conjectural symmetry that categorifies the "Perverse = Hodge" identity, verifying it in specific cases through connections with variations of Hodge structures, Hilbert schemes, and Looijenga-Lunts-Verbitsky Lie algebras.
This paper establishes the necessary and sufficient conditions on the parameters , , and for the existence of a balanced generalized de Bruijn sequence, defined as a cyclic binary sequence with an equal number of 0s and 1s where every substring of length appears at most times.
This paper introduces the concept of quasi-isospectrality as a generalization of isospectrality, reviews existing results, applies the BMT method to construct quasi-isospectral Sturm-Liouville operators, and establishes that any two quasi-isospectral closed manifolds of odd dimension are necessarily isospectral while extending classical compactness results to this new setting.
The authors prove the existence and uniqueness of a rigid, slope-stable rank 4 vector bundle with specific Chern classes on general polarized hyperkähler fourfolds of Kummer type satisfying certain divisibility conditions, thereby extending previous results from -type varieties and aiming to explicitly describe a locally complete family of such fourfolds.
This paper generalizes Bruhat-Tits theory to higher-dimensional bases by defining and proving the schematic nature of -bounded subgroups associated with concave functions on root systems, thereby constructing smooth group schemes adapted to normal crossing divisors and extending these results to mixed characteristic settings with applications to wonderful embeddings and surface singularities.
This paper investigates the deformation theory of local Calabi-Yau manifolds, specifically focusing on crepant resolutions of isolated rational Gorenstein singularities in dimension three to derive partial classification results for canonical threefold singularities, while also examining a noncrepant example involving the blowup of a small resolution.
This paper establishes an equivalence between crystals on the prismatic site and modules with integrable quasi-nilpotent -connections, demonstrating that their cohomology is computed by a -de Rham complex and providing a geometric construction of the prismatic Sen operator that yields an explicit description of the action of on de Rham cohomology.
This paper investigates algebraically coisotropic submanifolds in holomorphic symplectic projective manifolds, proving that when the ambient space is an abelian variety or the submanifold has a semi-ample canonical bundle, the pair decomposes into a product involving a Lagrangian submanifold, while also noting the non-existence of such Lagrangian submanifolds on sufficiently general abelian varieties.