Ulrich Bundles on Intersections of Two 4-Dimensional Quadrics

Abstract

In this paper, we investigate the moduli space of Ulrich bundles on a smooth complete intersection of two 4-dimensional quadrics in P-5. The main ingredient is the semiorthogonal decomposition by Bondal-Orlov, combined with the categorical methods pioneered by Kuznetsov and Lahoz-Macri-Stellari. Using these methods, we prove that any smooth intersection of two 4-dimensional quadrics in P-5 carries an Ulrich bundle of rank r for every r >= 2. Moreover, we provide a description of the moduli space of stable Ulrich bundles.