Relative singular locus and Balmer spectrum of matrix factorizations
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- by Yuki Hirano PDF
- Trans. Amer. Math. Soc. 371 (2019), 4993-5021 Request permission
Abstract:
For a separated Noetherian scheme $X$ with an ample family of line bundles and a non-zero-divisor $W\in \Gamma (X,L)$ of a line bundle $L$ on $X$, we classify certain thick subcategories of the derived matrix factorization category $\textrm {DMF}(X,L,W)$ of the Landau–Ginzburg model $(X,L,W)$. Furthermore, by using the classification result and the theory of Balmer’s tensor triangular geometry, we show that the spectrum of the tensor triangulated category $(\textrm {DMF}(X,L,W), \otimes ^{\frac {1}{2}})$ is homeomorphic to the relative singular locus $\mathrm {Sing}(X_0/X)$, introduced in this paper, of the zero scheme $X_0\subset X$ of $W$.References
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Additional Information
- Yuki Hirano
- Affiliation: Department of Mathematics, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan
- Email: y.hirano@math.kyoto-u.ac.jp
- Received by editor(s): March 2, 2017
- Received by editor(s) in revised form: January 4, 2018
- Published electronically: August 30, 2018
- Additional Notes: The author was a Research Fellow of Japan Society for the Promotion of Science and was partially supported by Grant-in-Aid for JSPS Fellows No.26-6240.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 4993-5021
- MSC (2010): Primary ~14F05, 18E30; Secondary ~14B05, 32S05
- DOI: https://doi.org/10.1090/tran/7509
- MathSciNet review: 3934475