Ulrich Sheaves on the Hilbert Square of K3 and Abelian Surfaces

Anindya Mukherjee; Pabitra Barik

doi:10.48550/arxiv.2602.01218

Ulrich Sheaves on the Hilbert Square of K3 and Abelian Surfaces

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Anindya Mukherjee, Pabitra Barik

DOI: 10.48550/arxiv.2602.01218

Cited by: 0

Abstract

We prove the existence of Ulrich sheaves on the Hilbert scheme of two points on a polarized K3 surface or an abelian surface. The construction proceeds by descending Ulrich bundles on the surface to the symmetric square and lifting them to the Hilbert square via the crepant Hilbert--Chow resolution. Finally, we estimate a bound for Ulrich complexity of the Hilbert Square.

Fields of Study & Subjects

Algebraic Geometry and Number Theory Geometry and complex manifolds Algebraic structures and combinatorial models

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 1 February 2026
Document type: Preprint