Methods and Applications of Analysis

Volume 25 (2018)

Number 4

In Memory of Professor John N. Mather: Part 2 of 3

Guest Editors: Sen Hu, University of Science and Technology, China; Stanisław Janeczko, Polish Academy of Sciences, Poland; Stephen S.-T. Yau, Tsinghua University, China; and Huaiqing Zuo, Tsinghua University, China.

Braid monodromy computation of real singular curves

Pages: 371 – 408

DOI: https://dx.doi.org/10.4310/MAA.2018.v25.n4.a7

Authors

Shmuel Kaplan (Department of Mathematics and Statistics, Bar-Ilan University, Ramat-Gan, Israel)

Eran Liberman (Department of Mathematics and Statistics, Bar-Ilan University, Ramat-Gan, Israel)

Mina Teicher (Department of Mathematics and Statistics, Bar-Ilan University, Ramat-Gan, Israel)

Abstract

We generalize the Moishezon–Teicher algorithm that was suggested for the computation of the braid monodromy of an almost real curve. The new algorithm suits a larger family of curves, and enables the computation of braid monodromy not only of caspidal curves, but of general algebraic curves, with some non simple singularities. Moreover, it works also when in the fiber the curve admits any number of imaginary points. We also provide two examples of how to use the generalized algorithm.

Keywords

singularities, braid monodromy

2010 Mathematics Subject Classification

14-xx

Full Text (PDF format)

This paper is part of the first and second authors’ PhD. thesis at Bar-Ilan University.

The authors were partially supported by the Emmy Noether Research Institute for Mathematics, Bar-Ilan University and the Minerva Foundation, Germany; by the Excellency Center “Group theoretic methods in the study of algebraic varieties” of the National Science Foundation of Israel; and by Eager, European Algebraic Geometry Research.

Received 19 October 2018

Accepted 22 August 2019

Published 1 November 2019