Computing Euler Obstruction Functions Using Maximum Likelihood Degrees. (16th October 2020)

• Record Type: Journal Article
• Authors: Rodriguez, Jose Israel; Wang, Botong
• Is Part Of: International mathematics research notices. Volume 2020:Number 20(2020)
• Page Start: 6699
• Page End: 6712
• Publication Date: 2020-10-16
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnz243
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: We give a numerical algorithm computing Euler obstruction functions using maximum likelihood degrees. The maximum likelihood degree is a well-studied property of a variety in algebraic statistics and computational algebraic geometry. In this article we use this degree to give a new way to compute Euler obstruction functions. We define the maximum likelihood obstruction function and show how it coincides with the Euler obstruction function. With this insight, we are able to bring new tools of computational algebraic geometry to study Euler obstruction functions.