On Derived Categories of Generalized Grassmannian Flips

2023/09/20 by Leung, Naichung Conan, Xie, Ying
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.2309.11136

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 ℙ^m× ℙⁿ 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, 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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