Hybrid models for homological projective duals and noncommutative resolutions

Jirui Guo Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China Mauricio Andrés Romo Jorquera Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

Algebraic Geometry arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2207.45002

arXiv, 2021.12
We study hybrid models arising as homological projective duals (HPD) of certain projective embeddings f:X→P(V) of Fano manifolds X. More precisely, the category of B-branes of such hybrid models corresponds to the HPD category of the embedding f. B-branes on these hybrid models can be seen as global matrix factorizations over some compact space B or, equivalently, as the derived category of the sheaf of A-modules on B, where A is an A_∞ algebra. This latter interpretation corresponds to a noncommutative resolution of B. We compute explicitly the algebra A by several methods, for some specific class of hybrid models, and find that in general it takes the form of a smash product of an A_∞ algebra with a cyclic group. Then we apply our results to the HPD of f corresponding to a Veronese embedding of projective space and the projective embedding of Fano complete intersections in P^n.
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@inproceedings{jirui2021hybrid,
  title={Hybrid models for homological projective duals and noncommutative resolutions},
  author={Jirui Guo, and Mauricio Andrés Romo Jorquera},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220706143533067910544},
  booktitle={arXiv},
  year={2021},
}
Jirui Guo, and Mauricio Andrés Romo Jorquera. Hybrid models for homological projective duals and noncommutative resolutions. 2021. In arXiv. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220706143533067910544.
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