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arXiv · 2309.11136

On Derived Categories of Generalized Grassmannian Flips

Naichung Conan Leung·Ying Xie
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Abstract

In this paper, we construct and classify a new family of flips, called generalized Grassmannian flips, by generalizing the construction of standard flips for $\mathbb{P}^m\times \mathbb{P}^n$ to any generalized Grassmannian $G/P$, where $P$ is a maximal parabolic subgroup of a complex semi-simple algebraic group. In addition, we show that a 9-fold generalized Grassmannian flip for $Sp(6, \mathbb{C})$ satisfies the DK flip conjecture by Bondal-Orlov and Kawamata via mutation techniques by Kuznetsov and Thomas' chess game method.

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Naichung Conan Leung, Ying Xie. 2023-09-20. On Derived Categories of Generalized Grassmannian Flips. https://arxiv.org/abs/2309.11136

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