Moore Matrices and Ulrich Bundles on an Elliptic Curve

Abstract

We give normal forms of determinantal representations of a smooth projective plane cubic in terms of Moore matrices. Building on this, we exhibit matrix factorizations for all indecomposable vector bundles of rank 2 and degree 0 without nonzero sections, also called Ulrich bundles, on such curves.

19 pages

Cited by in corpus (3)

• A positive proportion of cubic curves over Q admit linear determinantal representations
• Branched covers and matrix factorizations
• Linear determinantal representations of smooth plane cubics over finite fields