Methods and Applications of Analysis

Volume 24 (2017)

Number 1

Special issue dedicated to Henry B. Laufer on the occasion of his 70th birthday: Part 1

Guest Editors: Stephen S.-T. Yau (Tsinghua University, China); Gert-Martin Greuel (University of Kaiserslautern, Germany); Jonathan Wahl (University of North Carolina, USA); Rong Du (East China Normal University, China); Yun Gao (Shanghai Jiao Tong University, China); and Huaiqing Zuo (Tsinghua University, China)

Logarithmic differential forms on Cohen–Macaulay varieties

Pages: 11 – 32

DOI: https://dx.doi.org/10.4310/MAA.2017.v24.n1.a2

Author

A. G. Aleksandrov (Institute for Control Sciences, RAS, Moscow, Russia)

Abstract

The purpose of the paper is to introduce a notion of logarithmic differential forms on singular varieties. We also compute the Poincaré series and generators of the corresponding modules in a few particular cases, including quasihomogeneous complete intersections, normal varieties, determinantal varieties, and others.

Keywords

logarithmic differential forms, de Rham complex, graded singularities, Poincaré series, complete intersections, normal varieties, determinantal varieties, fans

2010 Mathematics Subject Classification

14F10, 14F40, 32S25, 58K45, 58K70

Full Text (PDF format)

Received 30 March 2016

Published 18 August 2017