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Algorithms for computing mixed multiplicities, mixed volumes, and sectional Milnor numbers

Kriti Goel, Vivek Mukundan, Sudeshna Roy and Jugal Verma
Vol. 13 (2023), 1–12
DOI: 10.2140/jsag.2023.13.1
Abstract

We present a package MixedMultiplicity for computing mixed multiplicities of ideals in a Noetherian ring which is either local or a standard graded algebra over a field. This enables us to find mixed volumes of convex lattice polytopes and sectional Milnor numbers of hypersurfaces with an isolated singularity. The algorithms make use of the defining equations of the multi-Rees algebra of ideals, which are obtained by generalising a result of Cox, Lin and Sosa.

Keywords
multi-Rees algebras, mixed multiplicities, sectional Milnor numbers, mixed volume
Mathematical Subject Classification
Primary: 13-04, 13A30, 13H15
Supplementary material

Macaulay2 package for computing mixed multiplicities of ideals
Milestones
Received: 14 August 2020
Revised: 19 May 2023
Accepted: 6 June 2023
Published: 28 August 2023
Authors
Kriti Goel
Department of Mathematics
University of Utah
Salt Lake City, UT
United States
Vivek Mukundan
Department of Mathematics
Indian Institute of Technology Delhi
Delhi
India
Sudeshna Roy
Department of Mathematics
Chennai Mathematical Institute
Kelambakkam
India
Jugal Verma
Department of Mathematics
Indian Institute of Technology Bombay
Mumbai
India
© 2023 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers).