Stable mappings and logarithmic relative symplectic forms
type: Item
instance of: scholarly article
title: Stable mappings and logarithmic relative symplectic forms
zbMATH Open document ID: 0930.32018
DOI: 10.1007/PL00004748
author: Martin P. Holland
author: David Mond
published in: Mathematische Zeitschrift
publication date: 1999-09-14T00:00:00Z
review text: Let \(D\) be the image of a stable, weighted homogeneous map \(f: \mathbb{C}^n \to\mathbb{C}^{n+1}\), with \(\dim_\mathbb{C} \text{Ker} (df_0)=1\), and which is not a trivial deformation of a lower-dimensional map. By proving a variant of the Buchsbaum-Eisenbud structure theorem for grade 3 Gorenstein quotients, we show the existence of a form \(\omega\in \Omega^2 (\log D)\) which restricts to a non-degenerate holomorphic 2-form on the Milnor fibres of \(D\); for small values of \(n\), calculations with the computer algebra system Macaulay show that this restriction is closed, and is thus a holomorphic symplectic form. We conjecture that this is always the case.
Mathematics Subject Classification ID: 32S55
Mathematics Subject Classification ID: 58K25
Mathematics Subject Classification ID: 58K05
zbMATH DE Number: 1336867
zbMATH Keywords: stable mappings
zbMATH Keywords: logarithmic relative symplectic forms
describes a project that uses: Macaulay2
MaRDI profile type: Publication
full work available at URL: pl00004748
OpenAlex ID: W2003067856
description: scientific article; zbMATH DE number 1336867