Nodal quintic del Pezzo threefolds and their derived categories

TL;DR

This paper constructs a semiorthogonal decomposition for the derived category of nodal quintic del Pezzo threefolds, linking their geometry to derived categories of finite-dimensional algebras via birational maps to quadric surface fibrations.

Contribution

It introduces a Kawamata type semiorthogonal decomposition for these threefolds, connecting their derived categories to algebraic structures through explicit birational transformations.

Findings

Decomposition of derived categories into finite-dimensional algebra components

Explicit birational maps to quadric surface fibrations

Framework applicable to nodal quintic del Pezzo threefolds

Abstract

We construct a Kawamata type semiorthogondal decomposition for the bounded derived category of coherent sheaves of nodal quintic del Pezzo threefolds, decomposing the bounded derived category into bounded derived categories of finite dimensional algebras. This is achieved by constructing birational maps from nodal quintic del Pezzo threefolds to quadric surface fibrations over the projective line.