Irregular fibrations of derived equivalent varieties

TL;DR

This paper investigates how irregular fibrations of algebraic varieties behave under derived equivalences, establishing invariance of certain fibrations and their fibers, thus deepening understanding of derived categories in algebraic geometry.

Contribution

It proves the derived invariance of irregular fibrations over varieties of general type and shows derived equivalences induce equivalences between their fibers.

Findings

Derived invariance of irregular fibrations over general type varieties

Derived equivalences induce equivalences between fibers

Extension of irrational pencil results to higher genus cases

Abstract

We study the behavior of irregular fibrations of a variety under derived equivalence of its bounded derived category. In particular we prove the derived invariance of the existence of an irregular fibration over a variety of general type, extending the case of irrational pencils onto curves of genus $g\geq 2$. We also prove that a derived equivalence of such fibrations induces a derived equivalence between their general fibers.