Computing the monodromy and pole order filtration on Milnor fiber cohomology of plane curves. (March 2019)

• Record Type: Journal Article
• Authors: Dimca, Alexandru; Sticlaru, Gabriel
• Is Part Of: Journal of symbolic computation. Volume 91(2019)
• Page Start: 98
• Page End: 115
• Publication Date: 2019-03
• Subjects: primary 32S40 -- secondary 32S22 32S55; Plane curve -- Milnor fiber -- Monodromy -- Pole order filtration -- b-Function; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.06.015
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We describe an algorithm computing the monodromy and the pole order filtration on the Milnor fiber cohomology of any reduced projective plane curve C . The relation to the zero set of Bernstein–Sato polynomial of the defining homogeneous polynomial for C is also discussed. When C has some non-weighted homogeneous singularities, then we have to assume that a conjecture holds in order to get some of our results. In all the examples computed so far this conjecture holds.