Year: 2026
Type: preprint
Abstract: Let $A$ be a complex abelian variety with $\NS(A)=\Z[L]$, $L$ ample. We show that a vector bundle filtered by line bundles splits uniquely into unipotent blocks, determine when it is ACM with respect to $L$, and show that it is never Ulrich. For a rank-two Ulrich bundle we bound from below the degree of the defect of every saturated line subbundle, compute the Hilbert polynomial of the defect, and show that the bound is attained exactly when an explicit cohomological support locus is nonempty. On abelian surfaces this locus is an ample curve in $\Pic^0(A)$; as a consequence, every rank-two Ulrich bundle is a Serre extension of a fixed numerical type, which we characterize and construct for every ample $L$. For $g\ge3$, we reduce the equality case to the existence of subcanonical codimension-two subschemes with prescribed cohomology.
Source: arXiv (Cornell University)
Author: Mondal, Soham
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202166961