Dominance of a Rational Map to the Coble Quartic

TL;DR

This paper demonstrates the dominance of a restriction map from a moduli space of stable sheaves on the projective plane to the Coble quartic, linking sheaf theory and algebraic geometry.

Contribution

It establishes the dominance of the restriction map and interprets stable sheaves via hyperplane arrangements, opening new avenues to study the Coble quartic's geometry.

Findings

Proves the dominance of the restriction map.

Provides a new interpretation of stable sheaves.

Suggests potential for further geometric investigations.

Abstract

We show the dominance of the restriction map from a moduli space of stable sheaves on the projective plane to the Coble quartic. With the dominance and the interpretation of a stable sheaf on the plane in terms of the hyperplane arrangements, we expect to investigate the geometry of the Coble quartic.