1351 papers
This paper classifies nondegenerate categories with a reductive group action entirely in terms of the group's root datum and applies these methods to establish a monoidal equivalence for bi-Whittaker -modules and provide evidence for a conjecture regarding the parabolic restriction of very central sheaves.
This paper establishes that Du Bois singularities descend under cyclically pure maps of Noetherian -algebras, a result that extends to log canonical singularities in the complex setting and yields new insights in prime and mixed characteristics.
This paper establishes that a smooth projective curve over satisfies a local-to-global variant of Grothendieck's Section Conjecture if it fulfills Kim's Conjecture for almost all auxiliary primes, thereby providing a new computational strategy that is successfully applied to the thrice-punctured line over .
This paper constructs (Q,W)-configurations of spherical objects in the derived categories of 3-fold crepant resolutions to demonstrate that the cases and admit faithful algebraic braid twist group actions of types D and E, respectively, thereby illustrating how specific geometric data gives rise to these exceptional Lie type patterns.
This paper proves the rationality of cohomological descendent generating series for Quot schemes on smooth projective surfaces with geometric genus zero, utilizing a Pandharipande-Thomas type wall-crossing recursion and a factorization through pure Quot theory involving explicit zero-dimensional correction operators.
This paper establishes a correspondence between the genus 0 descendant Gromov-Witten theories of two varieties related by a simple flop and demonstrates that this correspondence is compatible with the Fourier-Mukai equivalence induced by the flop.
This paper examines the arithmetic and Hodge-theoretic properties of the isomorphisms in the decomposition theorem for the quantum cohomology of blowups, which are essential for addressing rationality questions raised by Katzarkov, Kontsevich, Pantev, and Yu.
This paper establishes a framework for Riemannian geometry on associative varieties by generalizing classical algebraic varieties to arbitrary fields, defining local representations for simple modules in associative algebras, and utilizing smooth function algebras to introduce connections and geodesic curves into non-commutative settings.
The paper establishes that the complete diagonal of the Laurent series expansion of a nondegenerate rational function in complex variables admits analytic continuation throughout the complex torus, excluding only a specific Landau variety constructed from the discriminants of the denominator's face truncations.
This note rectifies the proof of Theorem 3.11 from a previous work on double Danielewski surfaces and concludes with a set of examples illustrating various cases.
Motivated by Hartogs' theorem, this paper establishes two rigidity results in complex geometry: first, that fiber-wise distributional solutions to algebraic linear differential equations upgrade to global holomorphic solutions under specific transverse conditions, and second, that continuous, fiber-wise holomorphic maps of degree 1 from a Kobayashi hyperbolic manifold fibered over to a projective variety are bi-holomorphic isomorphisms if injective on a very ample hypersurface.
This paper establishes that the asymptotic behavior of two competing notions of rank for linear series on tropical curves is governed by a single invariant analogous to algebraic volumes, while also demonstrating the compatibility of tropical volume with the tropicalization of curves.
The paper establishes a construction that generates -torsion elements in the class group of a specific number field by utilizing -torsion points from the Jacobian of an -gonal curve.
This paper classifies non-commutative crepant resolutions (NCCRs) of anticanonical cones over del Pezzo surfaces by showing they arise from geometric helices and proving that all such helices are connected via mutations, up to simple operations, using associated polygons as a key tool.
This paper introduces GlobalCY, a JAX-based framework demonstrating that globally defined, symmetry-aware neural Kähler potential models outperform local-input baselines on challenging Calabi–Yau geometries by significantly reducing geometric inconsistencies like negative-eigenvalue frequency and projective-invariance drift.
This paper analyzes the singular central fiber of the Donaldson--Friedman construction for twistor spaces of connected sums as a Ferrand pushout, explicitly describing its Chow ring and deriving specialization formulas and gluing constraints, while interpreting the local geometry via Kato--Nakayama spaces and establishing additivity results for characteristic classes of associated bundles.
This paper constructs an analogue of irreducible cuspidal representations for $PGL(2)$ over a two-dimensional local field using quadratic extensions and non-Galois-invariant characters, demonstrating that while the construction parallels the classical case, the resulting representations exhibit distinct behavior upon restriction to the Borel subgroup and motivating a generalized definition of cuspidality for split reductive groups.
This paper investigates curves on the product of two -trivial surfaces and establishes that the minimal genus of a non-trivial curve on the product of two very general abelian surfaces is 6.
This paper establishes a natural injective correspondence between numerical tropical line bundles on a very affine variety and toric b-divisors on its tropicalization, demonstrating that this map restricts to a bijection between the tropical nef cone and tropically nef b-Cartier divisors, thereby generalizing Baker's specialization to higher dimensions and clarifying the birational nature of tropical line bundles.
This paper extends Gaitsgory and Rozenblyum's result on derived arc spaces by demonstrating that, similar to smooth schemes, the derived arc spaces of reduced local complete intersection schemes are equivalent to their classical counterparts.