Singularities on complex hypersurfaces of a fixed degree
type: Item
instance of: scholarly article
title: Singularities on complex hypersurfaces of a fixed degree
zbMATH Open document ID: 1367.32024
author: E. A. Astashov
published in: Journal of Mathematical Sciences (New York)
publication date: 2015-10-23T00:00:00Z
review text: In this paper the author studies \(\mathcal{A}_{k}\)-singularities on algebraic hypersurfaces of fixed degree in \(\mathbb{C}^{n}\). Let \(k_{n}(d)\) be the largest \(k \in \mathbb{N}\) such that there exists a hypersurface of degree \(d\) in \(\mathbb{C}^{n}\) with an \(\mathcal{A}_{k}\)-singularity at some point. The author studies the asymptotic behavior of \(k_{n}(d)\) as \(d \to \infty\). An asymptotic estimate for the Milnor number in this context is presented.
Mathematics Subject Classification ID: 32S25
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14J17
zbMATH DE Number: 6497496
zbMATH Keywords: \(\mathcal{A}_{k}\) singulatity
zbMATH Keywords: algebraic hypersurfaces
zbMATH Keywords: Milnor number
reviewed by: Nivaldo G. Jun Grulha
MaRDI profile type: Publication
full work available at URL: s10958-015-2418-1
OpenAlex ID: W608708317
cites work: Plane curves of minimal degree with prescribed singularities
cites work: Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi
cites work: Singularities of type \(A_k\) on plane curves of a chosen degree
cites work: An effective Łojasiewicz inequality for real polynomials
DOI: 10.1007/S10958-015-2418-1
description: scientific article; zbMATH DE number 6497496