Ulrich bundles on Fano and Calabi–Yau double covers of P^3

Abstract: Motivated by Ulrich’s work on Cohen–Macaulay modules, Eisenbud and Schreyer asked whether every projective variety admits a sheaf whose cohomology table is as simple as possible, namely, a multiple of the cohomology table of the structure sheaf of projective space. In this talk, I will discuss existence results for such sheaves on cyclic coverings of P^n, showing how they arise from matrix factorisations of the equations of the branch loci, and on Fano threefolds, exploiting the rich geometry of these varieties. In particular, I prove that Fano and Calabi–Yau double covers of P^3 carry rank‑2 Ulrich sheaves, and describe some features of their moduli spaces.

algebraic geometry

Audience: researchers in the topic

SISSA algebraic geometry seminar