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arXiv · 2303.15382

Tensor triangulated category structures in the derived category of a variety with big (anti-)canonical bundle

Angel Israel Toledo Castro
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Abstract

Let $X$ be a smooth projective variety over $\mathbb{C}$ with big (anti-)canonical bundle. It is known that in this situation the Balmer spectrum of the tensor triangulated category of perfect complexes $Perf(X)$ of $X$ equipped with the derived tensor product $\otimes_{X}^{\mathbb{L}}$ recovers the space $X$. In this work we study the possible tensor triangulated category structures one can put on $Perf(X)$. As an application we prove a monoidal version of the well-known Bondal-Orlov reconstruction theorem.

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Angel Israel Toledo Castro. 2023-03-27. Tensor triangulated category structures in the derived category of a variety with big (anti-)canonical bundle. https://doi.org/10.2140/pjm.2023.327.359

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