4 citations · 10 across the 10 of their papers we have counts for
12 papers
NEXP-Completeness of Existential Presburger Arithmetic with Divisibility
Ignacio Barros, Michaël Cadilhac, Guillermo A. Pérez
We prove that satisfiability for existential Presburger arithmetic with divisibility (EPAD) is NEXP-hard. Together with the known NEXP upper bound, this establishes NEXP-completene…
IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation
Johannes Schmitt, Gergely Bérczi, Jasper Dekoninck +57
As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of…
A simple criterion for the uniruledness of an orthogonal modular variety
Ignacio Barros
We exhibit a simple uniruledness criterion for general orthogonal modular varieties in terms of invariants of the corresponding lattice. As an application, we obtain the uniruledne…
On the irrationality of moduli spaces of projective hyperkähler manifolds
Daniele Agostini, Ignacio Barros, Kuan-Wen Lai
The aim of this paper is to estimate the irrationality of moduli spaces of hyperkähler manifolds of types K3, Kum, OG6, and OG10. We prove that the degrees of irratio…
Kodaira dimension of moduli spaces of hyperkähler varieties
Ignacio Barros, Pietro Beri, Emma Brakkee +1
We study the Kodaira dimension of moduli spaces of polarized hyperkähler varieties deformation equivalent to the Hilbert scheme of points on a K3 surface or to O'Grady's ten dimens…
The Kodaira classification of the moduli of hyperelliptic curves
Ignacio Barros, Scott Mullane
We study the birational geometry of the moduli spaces of hyperelliptic curves with marked points. We show that these moduli spaces have non -factorial singularities. We…
On the irrationality of moduli spaces of K3 surfaces
Daniele Agostini, Ignacio Barros, Kuan-Wen Lai
We study how the degrees of irrationality of moduli spaces of polarized K3 surfaces grow with respect to the genus . We prove that the growth is bounded by a polynomial function…
Pencils on surfaces with normal crossings and the Kodaira dimension of
Daniele Agostini, Ignacio Barros
We study smoothing of pencils of curves on surfaces with normal crossings. As a consequence we show that the canonical divisor of is not pseudo-effec…
On product identities and the Chow rings of holomorphic symplectic varieties
Ignacio Barros, Laure Flapan, Alina Marian +1
For a moduli space of stable sheaves over a surface , we propose a series of conjectural identities in the Chow rings gener…
Two moduli spaces of Calabi-Yau type
Ignacio Barros, Scott Mullane
We show and have Kodaira dimension zero. Our method relies on the construction of a number of curves via nodal Lefschetz penci…
Geometry of the moduli space of -pointed K3 surfaces of genus 11
Ignacio Barros
We prove that the moduli space of polarized surfaces of genus eleven with marked points is unirational when and uniruled when . As a consequence, we sett…
Uniruledness of Strata of Holomorphic Differentials in Small Genus
Ignacio Barros
We address the question concerning the birational geometry of the strata of holomorphic and quadratic differentials. We show strata of holomorphic and quadratic differentials to be…