Residues and Duality for Projective Algebraic Varieties
Residues and Duality for Projective Algebraic Varieties
复制标题
射影代数簇的留数和对偶性
DOI：
10.1090/ulect/047
复制
发表时间：
2008
影响因子：
0.6
通讯作者：
E. Kunz
中科院分区：
文献类型：
--
作者：
E. Kunz
这本书是由E.昆兹为学生在代数和代数几何的背景下，发展本地和全球的对偶理论在特殊情况下（可能奇异）代数簇代数封闭基地领域。它描述对偶和留数定理的卡勒微分形式和他们的残留物。残基的性质是通过局部上同调引入的。特别强调了留数与代数几何经典结果及其推广之间的关系。A.的贡献。迪肯斯坦给出应用程序的残留物和对偶多项式解决常系数偏微分方程和问题的插值和理想的成员资格。D. A.考克斯解释复曲面残基，并涉及到他们的早期文本。这本书的目的是作为一个介绍更先进的治疗和进一步的应用程序的主题，其中许多书目提示。
This book, which grew out of lectures by E. Kunz for students with a background in algebra and algebraic geometry, develops local and global duality theory in the special case of (possibly singular) algebraic varieties over algebraically closed base fields. It describes duality and residue theorems in terms of Kahler differential forms and their residues. The properties of residues are introduced via local cohomology. Special emphasis is given to the relation between residues to classical results of algebraic geometry and their generalizations. The contribution by A. Dickenstein gives applications of residues and duality to polynomial solutions of constant coefficient partial differential equations and to problems in interpolation and ideal membership. D. A. Cox explains toric residues and relates them to the earlier text. The book is intended as an introduction to more advanced treatments and further applications of the subject, to which numerous bibliographical hints are given.