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)

Residual algebraic restrictions of differential forms

Pages: 45 – 61



G. Ishikawa (Department of Mathematics, Hokkaido University, Japan)

S. Janeczko (Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland; and Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland)


We study germs of differential forms over singular varieties. The geometric restriction of differential forms to singular varieties is introduced and algebraic restrictions of differential forms with vanishing geometric restrictions, called residual algebraic restrictions, are investigated. Residues of plane curves-germs, hypersurfaces, Lagrangian varieties as well as the geometric and algebraic restriction via a mapping were calculated.


differential forms, singularities, geometric restriction, parametric curves

2010 Mathematics Subject Classification

Primary 53D05. Secondary 57R42, 58A10, 58K05.

The first author was partially supported by JSPS KAKENHI no. 15H03615.

The second author was partially supported by NCN grant no. DEC-2013/11/B/ST1/03080.

Received 2 April 2016

Published 18 August 2017