Counting aCM Toric Bundles of Rank Two on the Veronese Surface

Abstract

We define the isomorphism classes of torus-equivariant rank 2 arithmetically Cohen-Macaulay (aCM) vector bundles on the Veronese surface, up to a twist by the hyperplane class, and count them. Our approach makes use of Klyachko's description of toric vector bundles via filtrations and the associated cohomology computation. We also describe several representative bundles.