183 papers
This paper demonstrates that any parahoric group scheme over a henselian discretely valued field becomes reductive after a finite Galois extension, allowing it to be recovered as the smoothening of Galois invariants of a reductive model, a result that extends prior work to the wildly ramified case and confirms the Grothendieck–Serre conjecture for generically trivial parahoric torsors in sufficiently good residue characteristics.
This paper proposes a reinforcement learning framework with a probabilistic reward function and a Gaussian baseline to discover power-flow network configurations that yield a significantly higher number of equilibrium points than current computational algebra methods can identify.
This paper establishes the invariance of signed counts of real curves on toric surfaces under specific boundary conditions via a new relative refined tropical invariant, while demonstrating that this invariance fails when conjugate point pairs are placed in the interior.
This paper establishes a unified microlocal and derived-geometric framework that connects index theory and analytic torsion for nonlinear PDEs to BCOV invariants, moduli spaces, and quantum field theory through the integration of Spencer hypercohomology, microlocal sheaf theory, and factorization algebras.
This paper presents a self-contained exposition of enumerative geometry results for K3 surfaces, confirming key conjectures by Yau–Zaslow, Göttsche, and Katz–Klemm–Vafa without requiring prior knowledge of Gromov–Witten theory.
This paper uses numerical certification to construct a counterexample proving that two-dimensional discrete periodic Schrödinger operators are not Fermi isospectrally rigid, thereby disproving a long-standing conjecture regarding the irreducibility of Fermi varieties for nontrivial real-valued potentials.
This paper investigates "holes" in the effective cones of Calabi-Yau threefolds—divisor classes that are theoretically effective yet lack global sections—by providing examples, establishing existence conditions, characterizing their semigroup structure within toric hypersurfaces, and deriving moduli-dependent volume bounds.
This paper constructs group-theoretic analogues of Johnson/Morita cocycles for pro-l groups to define Galois-cohomological classes for smooth curves, which are then used to demonstrate the existence of a non-hyperelliptic curve whose Ceresa class has a torsion image under the l-adic Abel-Jacobi map.
This paper establishes that a compact Kähler manifold whose dual Kähler cone contains a rational interior point has a projective Albanese variety, thereby resolving the Oguiso–Peternell problem for Ricci-flat manifolds and addressing related algebraicity questions for threefolds.
This paper establishes that a quasi-compact Kähler manifold admitting a complex polarized variation of Hodge structures with zero-dimensional fibers is algebraically hyperbolic and satisfies the generalized big Picard theorem, while also demonstrating that a finite étale cover of such a manifold admits a compactification where the boundary complement is Picard hyperbolic and all non-boundary subvarieties are of general type.
This paper investigates the local cyclicity and the growth of rational point groups for isogeny classes of abelian varieties over finite fields characterized by Weil polynomials of the form , utilizing a specific criterion involving the coprimality of the polynomial's derivative and radical at .
This paper generalizes the Cattani-Deligne-Kaplan finiteness theorem for Hodge classes to self-dual classes in integral variations of Hodge structure by leveraging the definability of period mappings within the o-minimal structure .
This paper investigates triangular line arrangements on the projective plane by proving their combinatorics are always realized by Roots-of-Unity-Arrangements, establishing conditions for their freeness, and demonstrating that freeness is not determined solely by weak combinatorics.
This paper proposes a family of conjectural tautological relations in the moduli spaces of stable curves, characterized by tree-like stable graphs decorated with psi-classes, which imply fundamental properties of Dubrovin-Zhang and double ramification hierarchies and are proven for the cases of one marked point or genus zero.
This paper establishes that on specific projective threefolds, certain moduli spaces of 2-dimensional torsion sheaves form smooth bundles over Hilbert schemes, thereby deriving a wall-crossing formula that relates curve counting invariants to D4-D2-D0 brane counts and exploring their modular properties through the lens of S-duality and Noether-Lefschetz theory.
This paper provides a complete combinatorial classification of all modular compactifications of the universal Jacobian over via -functions, characterizing their geometric properties, isomorphism conditions, and structural relationships within an extended stability poset.
This paper establishes a combinatorial Hirzebruch-Riemann-Roch theorem for tropical vector bundles on toric varieties using Khovanskii-Pukhlikov theory and confirms that the Euler characteristic equals the rank of global sections for tautological bundles associated with matroids.
This paper proves that split reductive Bruhat-Tits group schemes over higher-dimensional bases are affine and introduces a new, more general construction of such schemes by extending J.-K. Yu's method and utilizing Néron-Raynaud dilatations alongside established techniques.
This paper establishes that the moduli of -valued constructible sheaves and perverse sheaves on a compact oriented manifold with a conically smooth stratification are -shifted Lagrangian, a result derived from constructing a relative left -Calabi--Yau structure via lax gluing of categorical cubes and identifying symplectic leaves for perverse sheaves with prescribed monodromy.
This paper constructs higher Chow cycles of type on a family of degree abelian covers of branched over points and proves that for a very general member, these cycles generate a subgroup of the indecomposable part of rank at least by computing their images under the transcendental regulator map.