170 papers
This paper investigates the monodromy representations of compact Lagrangian fibrations, proving their irreducibility over when the period map is generically immersive and characterizing the structure of these representations as a direct sum of two irreducible local systems in the isotrivial case.
This paper introduces the concept of Lorentzian proper position to characterize elementary quotients of M-convex functions and analyze the incidence geometry of tropical linear spaces, revealing that while certain classical incidence properties fail for general tropical spaces, they hold for those possessing adjoints.
This paper computes the height filtration and successive minima of the height function associated with a relatively ample line bundle on a flag bundle over a smooth projective curve defined over an algebraically closed field of positive characteristic.
This paper establishes a tropical analogue of Porteous' formula by developing characteristic classes for tropical vector bundles on rational polyhedral spaces with boundary, utilizing a splitting principle and the boundary framework to ensure degeneracy loci achieve their expected codimension.
This paper confirms Oort's conjecture by proving that for even and , every geometric generic member of the maximal supersingular Ekedahl-Oort stratum in the moduli space of principally polarized abelian varieties has an automorphism group consisting only of , while also establishing the result for the specific case of for any prime .
This paper establishes an almost equivalence between the equivariant Tamarkin category and the category of derived complete modules over the Novikov ring, thereby clarifying the relationship between Tamarkin's extra variable and Novikov rings.
This paper proves a conjecture by Raskind, Spiess, Colliot-Thélène, and Sansuc regarding the structure of the Chow group of zero-cycles on geometrically Kummer surfaces over -adic fields and provides the first unconditional evidence for a local-to-global principle for zero-cycles on such surfaces by demonstrating that the Brauer-Manin obstruction is the sole obstruction to weak approximation in specific cases.
This paper classifies all pairs consisting of a -bundle over a non-rational ruled surface and its relatively maximal connected automorphism group over an algebraically closed field of characteristic zero.
This paper investigates the asymptotic agreement and divergence between geometric and virtual counts of pointed curves with fixed complex structure in blow-ups of projective space, providing explicit formulas for toric cases via Jacobian integrals and computing virtual counts for using quantum cohomology.
This paper establishes that the decomposition theorem components for contraction maps of torus actions of complexity one are intersection cohomology complexes of even codimensional subvarieties, leading to the vanishing of odd-dimensional intersection cohomology for rational complete varieties of this type and providing explicit formulas for the Betti numbers of affine trinomial hypersurfaces based on their defining equations.
This paper presents a simple construction of algebro-geometric solutions to the Gelfand–Dickey hierarchy using an -type infinite ODE system and Dubrovin's method, while also deriving a formula for the -point function of the associated Riemann -function.
This paper generalizes a lower bound for the log canonical threshold of -primary ideals to the -threshold in positive characteristic and provides a classification of homogeneous ideals that achieve this minimal singularity threshold, thereby resolving a conjecture by Bivià-Ausina.
This paper establishes a framework for constructing Monge-Ampère measures and solving associated variational equations on balanced polyhedral spaces by leveraging convex function theory and tropical intersection, while also connecting these results to non-archimedean pluripotential theory.
This paper establishes the theorem of the heart for Weibel's homotopy -theory (), proving that the realization functor induces an equivalence for small stable -categories with bounded -structures, a result derived from a strengthened version of Barwick's theorem that provides precise isomorphism ranges for classical -theory and demonstrates the sharpness of these bounds.
This paper presents an algorithm to compute the image of the adelic Galois representation for elliptic curves over with complex multiplication (excluding -invariants 0 and 1728) and establishes new results regarding the entanglement of their division fields.
This paper demonstrates that for a symplectic manifold with a monoidal Fukaya category, the monoidal structure uniquely determines the homological mirror functor to the derived category of coherent sheaves on its mirror , thereby filling a gap in the literature regarding the reconstruction of the mirror from categorical data.
This paper establishes a toric analog of Yuan and Zhang's theory of adelic divisors to show that the arithmetic self-intersection number of a semipositive toric adelic divisor equals the integral of a concave function over a compact convex set, thereby enabling the computation of heights for toric arithmetic varieties with singular metrics.
This paper introduces the framework of non-Abelian patchworking, a geometric method for constructing real algebraic surfaces in via the real locus of non-Abelian complex-phase tropical hypersurfaces, which successfully reproduces all isotopy types of surfaces up to degree three and reveals that primitive surfaces can exhibit Euler characteristics distinct from their complex counterparts.
This paper generalizes Serre conjecture II to pseudo-reductive groups by proving its equivalence to the original conjecture for semisimple groups, thereby establishing that every torsor under a pseudo-semisimple, simply connected group over global function fields or non-archimedean local fields possesses a rational point.
This paper establishes that the graded Ehrhart theory of unimodular zonotopes yields a -evaluation of their Tutte polynomials and characterizes their harmonic algebras as finitely generated, Cohen--Macaulay coordinate rings of arrangement Schubert varieties, thereby confirming specific conjectures by Reiner and Rhoades.