Back to Search
Start Over
Derived Categories of Families of Sextic del Pezzo Surfaces
- Source :
- International Mathematics Research Notices. 2021:9262-9339
- Publication Year :
- 2019
- Publisher :
- Oxford University Press (OUP), 2019.
-
Abstract
- We construct a natural semiorthogonal decomposition for the derived category of an arbitrary flat family of sextic del Pezzo surfaces with at worst du Val singularities. This decomposition has three components equivalent to twisted derived categories of finite flat schemes of degrees 1, 3, and 2 over the base of the family. We provide a modular interpretation for these schemes and compute them explicitly in a number of standard families. For two such families the computation is based on a symmetric version of homological projective duality for $\mathbb{P}^2 \times \mathbb{P}^2$ and $\mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1$, which we explain in an appendix.<br />Comment: 48 pages; v2: minor improvements
- Subjects :
- Derived category
General Mathematics
Computation
010102 general mathematics
Duality (optimization)
01 natural sciences
Interpretation (model theory)
Combinatorics
Base (group theory)
Mathematics - Algebraic Geometry
Mathematics::Algebraic Geometry
0103 physical sciences
FOS: Mathematics
Gravitational singularity
010307 mathematical physics
0101 mathematics
Algebraic Geometry (math.AG)
Mathematics
Subjects
Details
- ISSN :
- 16870247 and 10737928
- Volume :
- 2021
- Database :
- OpenAIRE
- Journal :
- International Mathematics Research Notices
- Accession number :
- edsair.doi.dedup.....0fe7fabb854b35232cc47d245a88acde