184 papers
This paper utilizes the isomorphism between the six-dimensional nilpotence variety and within the pure spinor superfield formalism to classify and explicitly construct various six-dimensional supermultiplets, including vector, hyper, and supergravity multiplets, by associating them with line bundles and higher-rank equivariant vector bundles on projective spaces.
This paper establishes a relative Poincaré–Verdier duality for supermanifolds via Berezin fiber integration to rigorously define picture changing operators and prove the equivalence of component, superspace, and geometric formulations of 3d supergravity.
This paper describes the moduli space of semi-homogeneous vector bundles on an abelian variety with totally degenerate reduction via non-Archimedean uniformization, identifying its essential skeleton with a tropical analogue and constructing a surjective analytic morphism from the character variety of the analytic fundamental group to the moduli space of semistable vector bundles with vanishing Chern classes.
This paper establishes a purity theorem for -adic local systems on rigid-analytic varieties with semistable formal models by proving that such systems are semistable if and only if their restrictions to the irreducible components of the special fiber are semistable, utilizing analytic prismatic -crystals and a newly derived prismatic purity theorem.
This paper establishes a real analogue of the generalized trisecant lemma in the form of a trichotomy, characterizing the possible numbers of real intersection points between a real projective variety and a complementary dimension linear space, with specific applications to the identifiability and typical ranks in independent component analysis and tensor decomposition.
This paper investigates the rationality of geometrically rational real threefold bundles with connected real loci and vanishing intermediate Jacobian obstructions, employing unramified cohomology, birational rigidity, and explicit constructions to establish both negative and positive results.
This paper establishes closed formulae for the orbifold Euler characteristics of double ramification loci and their higher-rank generalizations in genus one, utilizing a recurrence relation to derive a polynomial result for rank one and a formula involving greatest common divisors of matrix minors for higher ranks.
This paper classifies, up to topological equivalence, the actions of the abelian group on compact Riemann surfaces of genus that yield a quotient of genus zero with a signature consisting of branch points of order .
This paper establishes that the degenerations of cohomological Hall algebras associated with 2-Calabi-Yau categories and preprojective algebras, with respect to the "less perverse" filtration, are isomorphic to the enveloping algebra of the current Lie algebra of the BPS Lie algebra, a result proven at the sheafified level and extended to torus-deformed settings to connect these structures with Maulik-Okounkov Yangians.
This paper establishes an explicit isomorphism between the equivariant nilpotent cohomological Hall algebra of one-dimensional sheaves on a surface resolving a Kleinian singularity and a completed positive half of the affine Yangian of the corresponding ADE Lie algebra, utilizing continuity theorems for -structures and multi-parameter Yangian definitions to characterize the algebra of cohomological Hecke operators.
This expanded lecture notes from the 2025 Lie-Stormer Summer School explore classical invariants by highlighting analogies between binary quartics and ternary cubics, presenting triangle groups in elliptic and hyperbolic settings, and discussing Hilbert's work on polynomials that are powers, supplemented by exercises and a section on Pfaffians.
This paper introduces the numerical invariants of birational and strong complete regularity for Fano type pairs using qdlt models and dual complexes, establishes their fundamental properties and connections to K-stability, and proves that maximal birational strong complete regularity implies 1-complementarity while the associated jumping thresholds satisfy the ascending chain condition.
This paper computes cohomological Chow groups of codimension one for varieties with isolated singularities, establishing results for higher-dimensional varieties with contractible dual complexes and for 3-dimensional varieties under the weaker condition that the second cohomology of the dual complex vanishes.
This paper establishes a short exact sequence relating the differential fundamental groupoids of a smooth family of varieties to its base and relative components, proving that for families of curves of genus at least 1, the resulting maps are isomorphisms that interpret Gauss-Manin connections via group cohomology and demonstrate that the total space becomes a de Rham after shrinking.
This paper establishes the existence of the minimal model program for arbitrary log canonical generalized pairs by introducing linearly decomposable pairs as a substitute for rational decompositions and proving the existence of flips without relying on the klt, NQC, or -factoriality conditions.
This paper refines the string equation on from the Chow ring to algebraic cobordism to derive inductive formulas for cobordism-valued psi-class intersections and explicit classes up to , including their images in -theory.
This paper constructs a principal twistor model for a crepant resolution of a conical symplectic variety and proves its universality in recovering asymptotic hyperkähler metrics, thereby establishing an inclusion of the corresponding moduli space into a finite-dimensional real vector space.
This paper provides a rigorous generalization of Rosenbloom and Tsfasman's algebraic-geometric codes to arbitrary genus curves by defining differential Goppa codes via -jets and Hasse-Schmidt derivatives, analyzing their structural properties and distance variations, and establishing that they encompass all linear codes on while strictly generalizing classical Goppa codes.
This paper develops a non-abelian, gauge-theoretic framework for the Schwarzian derivative and second-order differential equations on Riemann surfaces, applying it to generalize Dedekind's approach to higher-genus curves via matrix-valued equations on the Hodge bundle, analyze periods of cubic threefolds, and model mechanical mass-spring systems.
This thesis extends the relative -contractibility of Koras-Russell threefolds and their higher-dimensional prototypes to arbitrary Noetherian base schemes, thereby establishing the existence of the first known family of smooth "exotic" motivic spheres in dimensions that are -homotopic to, but not isomorphic to, the punctured affine space .