The homological projective dual of

Author:

Rennemo Jørgen Vold

Abstract

We study the derived category of a complete intersection $X$ of bilinear divisors in the orbifold $\operatorname{Sym}^{2}\mathbb{P}(V)$. Our results are in the spirit of Kuznetsov’s theory of homological projective duality, and we describe a homological projective duality relation between $\operatorname{Sym}^{2}\mathbb{P}(V)$ and a category of modules over a sheaf of Clifford algebras on $\mathbb{P}(\operatorname{Sym}^{2}V^{\vee })$. The proof follows a recently developed strategy combining variation of geometric invariant theory (VGIT) stability and categories of global matrix factorisations. We begin by translating $D^{b}(X)$ into a derived category of factorisations on a Landau–Ginzburg (LG) model, and then apply VGIT to obtain a birational LG model. Finally, we interpret the derived factorisation category of the new LG model as a Clifford module category. In some cases we can compute this Clifford module category as the derived category of a variety. As a corollary we get a new proof of a result of Hosono and Takagi, which says that a certain pair of non-birational Calabi–Yau 3-folds have equivalent derived categories.

Publisher

Wiley

Subject

Algebra and Number Theory

Reference42 articles.

1. [BO95] Bondal, A. and Orlov, D. , Semiorthogonal decomposition for algebraic varieties, Preprint (1995), arXiv:alg-geom/9506012v1.

2. Koszul duality and modular representations of semisimple Lie algebras

3. Equivariant resolution, linearization, and Hilbert's fourteenth problem over arbitrary base schemes

4. Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence;Positselski;Mem. Amer. Math. Soc.,2011

5. Representations of associative algebras and coherent sheaves;Bondal;Izv. Akad. Nauk SSSR Ser. Mat.,1989

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