Exceptional collections on some fake quadrics

TL;DR

This paper constructs maximal-length exceptional collections on certain complex surfaces, leading to new examples of quasiphantom categories, advancing understanding in algebraic geometry and derived categories.

Contribution

It introduces new maximal-length exceptional collections on specific surfaces of general type, and constructs quasiphantom categories as their orthogonal complements.

Findings

Constructed exceptional collections on four families of surfaces

Identified new quasiphantom categories

Enhanced understanding of derived categories of surfaces

Abstract

We construct exceptional collections of maximal length on four families of surfaces of general type with $p_g=q=0$ which are isogenous to a product of curves. From these constructions we obtain new examples of quasiphantom categories as their orthogonal complements.