Stability of tri-canonical curves of genus two
type: Item
instance of: scholarly article
title: Stability of tri-canonical curves of genus two
zbMATH Open document ID: 1111.14017
author: Donghoon Hyeon
author: Yongnam Lee
published in: Mathematische Annalen
publication date: 2007-01-26T00:00:00Z
review text: Let \(\overline{M}_2\) be the moduli space of stable curves of genus \(2\) and \(\overline{M}_2^{\text{ps}}\) be the moduli space of pseudo-stable curves of genus \(2\). Recall that a complete curve is pseudo-stable if it is connected, reduced, has only ordinary nodes and cusps as singularities, genus \(1\) subcurves meet the rest of the curve in \(2\) or more points and genus \(0\) subcurves meet the rest of the curve in \(3\) or more points. In the paper under review it is shown that: 1) A tri-canonically embedded complete curve of genus \(2\) is Chow semistable if and only if it is pseudo-stable, 2) There is a natural isomorphism between \(\overline{M}_2^{\text{ps}}\) and the compact moduli space of binary sextics, and 3) \(\overline{M}_2^{\text{ps}}\) is the log canonical model of the pair \((\overline{M}_2, \alpha \Delta _0+\frac{1+\alpha}2\Delta _1 +\frac 1 2 \Xi)\) for \(7/10<\alpha \leq 9/11\).
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 5118873
zbMATH Keywords: moduli spaces
zbMATH Keywords: pseudo-stable curves
zbMATH Keywords: log canonical model
reviewed by: Christopher Hacon
MaRDI profile type: Publication
full work available at URL: s00208-006-0046-2
OpenAlex ID: W2068421462
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DOI: 10.1007/S00208-006-0046-2
description: scientific article; zbMATH DE number 5118873