Holomorphic Koszul–Brylinski homologies of Poisson blow-ups

作     者：Xiaojun CHEN Youming CHEN Song YANG Xiangdong YANG 

作者机构：School of Mathematics Sichuan University School of Science Chongqing University of Technology Center for Applied Mathematics Tianjin University Department of Mathematics Lanzhou University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报(英文版))

年 卷 期：2025年

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by NSFC (Grant No. 11890660, 11890663, 12126309, 12126354, 12171351, 12271377, 12261131498,12271225) the Natural Science Foundation of Chongqing (No. CSTC2020JCYJ-MSXMX0160) the Natural Science Foundation of Tianjin (No. 20JCQNJC02000) 

摘      要：We derive a blow-up formula for holomorphic Koszul–Brylinski homologies of compact holomorphic Poisson manifolds. As applications, we investigate the invariance of the E1-degeneracy of the Dolbeault–Koszul–Brylinski spectral sequence under Poisson blow-ups, and compute the holomorphic Koszul–Brylinski homology for del Pezzo surfaces and two complex nilmanifolds with holomorphic Poisson structures.