Systems of polynomial equations defining hyperelliptic \(d\)-osculating covers
type: Item
instance of: scholarly article
title: Systems of polynomial equations defining hyperelliptic \(d\)-osculating covers
zbMATH Open document ID: 1359.14032
author: Armando Treibich
publication date: 2015-09-28T00:00:00Z
review text: Let \(X\) denote a fixed smooth projective curve of genus \(1\) defined over an algebraically closed field \(\mathbb{K}\) of arbitrary characteristic \(p\neq 2\). The author assumes the degree-2 projection \(\varphi: X \to {\mathbb P}^1\) ramified over \(\{\infty, 0, 1, \lambda\}\); \(X\) is expressed by \(y^2 = x(x-1)(x-\lambda)\) in the ordinary sense. As a typical case, by letting the affine coordinate \(x = P/Q\) where \(P\) and \(Q\) are certain polynomials over \({\mathbb P}^1\), there naturally appears a covering space of \(X\). Based on the covering space, the author investigates the moduli space \(H(X,n)\) of degree-\(n\) finite separable covers of \(X\) by hyperelliptic curves. It is related to a square system of polynomial equations. Furthermore, the author obtains nonsquare systems parameterizing hyperelliptic \(d\)-osculating covers for any \(d>1\).
reviewed by: Shigeki Matsutani
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 33E05
Mathematics Subject Classification ID: 13N10
Mathematics Subject Classification ID: 14M25
zbMATH DE Number: 6485784
zbMATH Keywords: hyperelliptic curves
zbMATH Keywords: \(d\)-osculating covers
zbMATH Keywords: Weierstrass points
MaRDI profile type: Publication
full work available at URL: s10688-015-0081-4
OpenAlex ID: W2038760901
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DOI: 10.1007/S10688-015-0081-4
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 6485784