Nodal quintic del Pezzo threefolds and their derived categories
Fei Xie

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Algebraic Geometry and Number Theory
