Modification of the Simpson moduli space M_{3m+1}(P_2) by vector bundles (I)

TL;DR

This paper constructs a compactification of the moduli space of stable vector bundles on plane curves with a specific Hilbert polynomial, by blowing up the Simpson moduli space, thus advancing the understanding of vector bundle moduli.

Contribution

It introduces a new compactification of the moduli space of stable vector bundles on plane curves with Hilbert polynomial 3m+1 via a blow-up of the Simpson moduli space.

Findings

Constructed a compactification of the moduli space.

Performed a blow-up of the Simpson moduli space.

Provided a geometric description of the new space.

Abstract

We consider the moduli space of stable vector bundles on curves embedded in P_2 with Hilbert polynomial 3m+1 and construct a compactification of this space by vector bundles. The result is a blow up of the Simpson moduli space M_{3m+1}(P_2).