178 papers
This paper proves the Shafarevich conjecture for very irregular varieties of dimension less than half that of their Albanese variety by combining the Lawrence-Venkatesh method with a big monodromy criterion.
This paper introduces a new moduli stack of "equinormalized curves" and establishes a stratification indexed by generalized dual graphs, where each stratum is described as a fiber bundle over a quotient of products of classical moduli spaces with explicitly computable fibers, thereby providing a detailed geometric characterization of the moduli of reduced curves with arbitrary singularities.
This paper characterizes multiplier ideals on normal schemes over via maps from pushforwards of dualizing sheaves under regular alterations, thereby providing a derived splinter characterization of klt singularities and an analogous description of test ideals in characteristic .
This paper establishes that the Chow motive of a specific smooth compactification of the Lagrangian fibration associated with a smooth cubic fourfold is a direct summand of the motive of the fifth power of the fourfold, thereby proving it is of abelian type for a general family of such cubics.
This paper presents a classification over the field of real numbers of the parametric line congruences arising from trilinear birational maps, utilizing line geometry tools to analyze the space-filling families of straight lines associated with these mappings.
This paper investigates cohomological and motivic invariants of semisimple algebraic groups within the Freudenthal magic square, establishing a new isotropy criterion for strongly inner groups of type based on the Rost invariant and constructing a degree 5 cohomological invariant that detects isotropy for certain groups of type .
This paper generalizes Pólya's theorem by proving that any polynomial strictly positive on the intersection of the nonnegative orthant and a specific level hypersurface can be represented by a polynomial with only positive coefficients, utilizing the Archimedean Representation Theorem.
This paper reviews the concept of Kalinin effectivity, establishes that wonderful compactifications of hyperplane arrangements and configuration spaces derived from Kalinin effective manifolds retain this property, and applies these results to demonstrate the effectivity of the Deligne-Mumford space of real rational curves and to investigate Smith-Thom maximality for Hilbert squares.
This paper classifies poor compact Kähler manifolds—those lacking rational curves and codimension-one analytic subvarieties—in dimensions up to three and in arbitrary dimensions under the condition that the Kodaira dimension is not , while also characterizing the locus of poor K3 surfaces within the period domain.
This paper establishes a complete proof of the Kobayashi-Hitchin correspondence for nef and big classes by introducing the concepts of adapted closed positive -currents and -adapted Hermitian-Yang-Mills metrics, thereby proving that a holomorphic vector bundle is slope polystable if and only if it admits such a metric, a result that extends to singular settings and yields new insights into projective flatness and the Bogomolov-Gieseker inequality.
This paper proves that for a specific class of Koras-Russell threefolds defined over an algebraically closed field of characteristic zero, the Chow groups are trivial, implying that all algebraic vector bundles over these varieties are trivial, with the additional result that their Chow-Witt groups are also trivial when a specific parameter is odd.
This paper investigates the geometric, algebraic, and analytic properties of hyperelliptic functions as a generalization of Jacobi elliptic functions and demonstrates their role as potential solutions to the nonlinear Schrödinger and complex modified Korteweg-de Vries equations.
This paper establishes three distinct representations for the flat space wavefunction derived from a graph , proving their correctness by linking the wavefunction to the canonical form of the cosmological polytope and confirming a conjecture regarding its partial fraction decomposition in terms of connected subgraphs.
This paper proves that for the standard triangle polygon (corresponding to the toric surface ), the spectral transform establishes a birational isomorphism between the Goncharov-Kenyon cluster integrable system and the Beauville integrable system by showing that it intertwines their respective Poisson structures, thereby demonstrating that Beauville integrable systems admit cluster algebra structures.
This paper proves that for a smooth complex projective curve of genus , the Fourier–Mukai transform of a semistable vector bundle with slope greater than $2g-2\mathrm{IT}_0$ property.
This paper extends the non-abelian Hodge correspondence to compact Kähler spaces with klt singularities by establishing an equivalence between polystable Higgs bundles and semi-simple flat bundles on regular loci and proving a descent theorem for Higgs bundles along resolutions, ultimately yielding a quasi-uniformization theorem for projective klt varieties satisfying the orbifold Miyaoka-Yau equality.
This paper extends the probabilistic construction of Kähler-Einstein metrics to Fano manifolds with non-discrete automorphism groups by introducing Gibbs polystability and symmetry-breaking via moment map constraints, conjecturing its equivalence to metric existence and the emergence of unique metrics in the large-N limit, while proving these results for log Fano curves and deriving a strengthened logarithmic Hardy-Littlewood-Sobolev inequality with optimal stability constants.
This paper defines a compactification of the parameter space for the quantum multiplication of hypertoric varieties, following deConcini and Gaiffi, and demonstrates how to extend this multiplication to the compactified space.
This paper introduces "Hodge atoms," new birational invariants constructed by combining rational Gromov-Witten invariants with Hodge theory via F-bundles, which are used to prove the irrationality of very general cubic fourfolds, reprove the equality of Hodge numbers for birational Calabi-Yau manifolds, and provide new obstructions to rationality over non-algebraically closed fields.
This paper advances Mazur's Program B for elliptic curves over by proving that the genus-69 modular curve has no non-CM rational points, a result achieved by linking these points to solutions of a generalized Fermat equation and reducing the complete classification of 7-adic Galois representations to finding rational points on a single plane quartic.