厦门大学学报（自然科学版）2023，Vol.62Issue(6)：948-962,15.DOI:10.6043/j.issn.0438-0479.202305016
代数几何和表示论的一些新进展
New advances in algebraic geometry and representation theory
摘要
Abstract
As a major research subfield of algebraic geometry,birational geometry studies the classification of projective algebraic varieties and their generalization as well as projective pairs under birational equivalence.After a brief introduction to the basic concepts in birational geometry,the first part of the survey explores the distribution and applications of the canonical volumes,which constitutes a key invariant in the boundedness problems of projective pairs.On the other hand,algebraic geometry and representation theory secure an inseparable connection,and symplectic singularities qualify as one of the important research topics that involve both fields.The second part of this article focuses on the deformation and quantization of symplectic singularities,as well as their applications in representation theory.关键词
对数一般型偶/有界性/典范体积/辛奇点/形变/半单群/约化群/幂零轨道/Harish-Chandra模/量子化/轨道方法Key words
log general type pair/boundednees/canonical volume/symplectic singularity/deformation/semisimple group/reductive group/nilpotent orbit/Harish-Chandra module/quantization/orbit method分类
数理科学引用本文复制引用
刘文飞,余世霖..代数几何和表示论的一些新进展[J].厦门大学学报（自然科学版）,2023,62(6):948-962,15.基金项目
国家自然科学基金(11971399,12131018,12001453) （11971399,12131018,12001453）
福建省自然科学基金(2022J06005) （2022J06005）
厦门大学校长基金(20720210006) （20720210006）
