Ulrich and Instanton Bundles on Special Cubic Fourfolds

TL;DR

This paper explores the relationship between instanton and Ulrich bundles on special cubic fourfolds, showing how low-rank instantons can deform into Ulrich bundles, influencing the geometry of the fourfolds.

Contribution

It demonstrates that acyclic extensions of instantons deform into Ulrich bundles and links the existence of low-rank instantons to the positioning of fourfolds within Hassett divisors.

Findings

Acyclic extensions of instantons deform into Ulrich bundles.

Existence of low-rank instantons implies fourfolds lie in Hassett divisors.

Analysis of divisors with discriminant 18 and 20.

Abstract

We study instanton and Ulrich bundles on hypersurfaces of the projective space, with a focus on special cubic fourfolds and generalized Pfaffians, notably defined by skew-symmetric endomorphisms of Steiner bundles. We prove that the acyclic extensions of instantons deform to Ulrich bundles and deduce that the existence of instantons of low rank and charge implies the existence of Ulrich bundles of low rank, which in turn forces the fourfold to lie in some Hassett divisor. Finally we take a closer look to divisors of cubics with discriminant 18 and 20.