Moduli of bundles on exotic del Pezzo orders

TL;DR

This paper studies the moduli space of line bundles on exotic del Pezzo orders, specifically maximal orders on the projective plane ramified on a smooth quartic, revealing it is either a point or a genus two curve.

Contribution

It computes possible Chern classes for line bundles on these orders and characterizes the moduli space structure.

Findings

Moduli space is either a point or a smooth genus two curve.

Chern classes for line bundles are explicitly computed.

Provides new insights into the geometry of exotic del Pezzo orders.

Abstract

Maximal orders of rank 4 on the projective plane, ramified on a smooth plane quartic are examples of exotic del Pezzo orders. We compute the possible Chern classes for line bundles on such orders and show the moduli space of line bundles with minimal second Chern class is either a point or a smooth genus two curve.