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Homogeneous ACM bundles on isotropic Grassmannians

  • Rong Du ORCID logo , Xinyi Fang ORCID logo EMAIL logo and Peng Ren ORCID logo
Published/Copyright: April 1, 2023

Abstract

In this paper, we characterize homogeneous arithmetically Cohen–Macaulay (ACM) bundles over isotropic Grassmannians of types 𝐵, 𝐶 and 𝐷 in terms of step matrices. We show that there are only finitely many irreducible homogeneous ACM bundles by twisting line bundles over these isotropic Grassmannians. So we classify all homogeneous ACM bundles over isotropic Grassmannians combining the results on usual Grassmannians by Costa and Miró-Roig. Moreover, if the irreducible initialized homogeneous ACM bundles correspond to some special highest weights, then they can be characterized by succinct forms.

MSC 2010: 14J60; 14F06; 14M17

Award Identifier / Grant number: 21JC1401900

Award Identifier / Grant number: 22DZ2229014

Funding statement: All of the authors are sponsored by Innovation Action Plan (Basic Research Projects) of Science and Technology Commission of Shanghai Municipality (Grant No. 21JC1401900) and Science and Technology Commission of Shanghai Municipality (Grant No. 22DZ2229014). The corresponding author is also sponsored by Jiangsu Funding Program for Excellent Postdoctoral Talent.

  1. Communicated by: Jan Frahm

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Received: 2022-05-17
Published Online: 2023-04-01
Published in Print: 2023-05-01

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