Corpus ID: 220969001

Derived categories of skew quadric hypersurfaces

  title={Derived categories of skew quadric hypersurfaces},
  author={Kenta Ueyama},
  journal={arXiv: Rings and Algebras},
  • Kenta Ueyama
  • Published 5 August 2020
  • Mathematics
  • arXiv: Rings and Algebras
The existence of a full strong exceptional sequence in the derived category of a smooth quadric hypersurface was proved by Kapranov. In this paper, we present a skew generalization of this result. Namely, we show that if $S$ is a standard graded $(\pm 1)$-skew polynomial algebra in $n$ variables with $n \geq 3$ and $f = x_1^2+\cdots +x_n^2 \in S$, then the derived category $\operatorname{\mathsf{D^b}}(\operatorname{\mathsf{qgr}} S/(f))$ of the noncommutative scheme $\operatorname{\mathsf{qgr… Expand
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