On the Rouquier dimension of wrapped Fukaya categories and a conjecture of Orlov

Author:

Bai Shaoyun,Côté Laurent

Abstract

We study the Rouquier dimension of wrapped Fukaya categories of Liouville manifolds and pairs, and apply this invariant to various problems in algebraic and symplectic geometry. On the algebro-geometric side, we introduce a new method based on symplectic flexibility and mirror symmetry to bound the Rouquier dimension of derived categories of coherent sheaves on certain complex algebraic varieties and stacks. These bounds are sharp in dimension at most$3$. As an application, we resolve a well-known conjecture of Orlov for new classes of examples (e.g. toric$3$-folds, certain log Calabi–Yau surfaces). We also discuss applications to non-commutative motives on partially wrapped Fukaya categories. On the symplectic side, we study various quantitative questions including the following. (1) Given a Weinstein manifold, what is the minimal number of intersection points between the skeleton and its image under a generic compactly supported Hamiltonian diffeomorphism? (2) What is the minimal number of critical points of a Lefschetz fibration on a Liouville manifold with Weinstein fibers? We give lower bounds for these quantities which are to the best of the authors’ knowledge the first to go beyond the basic flexible/rigid dichotomy.

Publisher

Wiley

Subject

Algebra and Number Theory

Reference96 articles.

1. Lagrangian skeleta of hypersurfaces in $$({\mathbb {C}}^*)^n$$

2. Symplectic homology I open sets in ℂ n

3. CS99 Chas, M. and Sullivan, D. , String topology, Preprint (1999), arXiv:math/9911159.

4. ST16 Shende, V. and Takeda, A. , Calabi–Yau structures on topological Fukaya categories, Preprint (2016), arXiv:1605.02721.

5. Syl19a Sylvan, Z. , Orlov and Viterbo functors in partially wrapped Fukaya categories, Preprint (2019), arXiv:1908.02317.

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A short proof of the Hanlon-Hicks-Lazarev Theorem;Forum of Mathematics, Sigma;2024

2. Rouquier dimension is Krull dimension for normal toric varieties;European Journal of Mathematics;2023-10-03

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