On the Picard group of the moduli scheme of stable curves in positive characteristic
type: Item
instance of: scholarly article
title: On the Picard group of the moduli scheme of stable curves in positive characteristic
zbMATH Open document ID: 0914.14012
DOI: 10.1016/S0022-4049(96)00118-1
author: E. Ballico
published in: Journal of Pure and Applied Algebra
publication date: 1998-02-25T00:00:00Z
review text: For every prime \(p\) let denote by \(M_g^-(p)\) the moduli scheme of stable curves of genus \(g\) over an algebraically closed field of characteristic \(p\). In this paper it is proved the following theorem: Fix an integer \(g\geq 5\) and a prime \(p> 84(g-1)\), then the Néron-Severi group \(\text{NS} (M_g^-(p))\) of \(M_g^-(p)\) is freely generated by the \([g/2]+2\) classes \(\lambda\) and \(\Delta_i\), \(0\leq i\leq [g/2]\). The proof uses a reduction to the characteristic 0 case (i.e. to the Harer's topological theorem) and a result by \textit{M. Pikaart} and \textit{A. J. de Jong} [The moduli space of curves, Proc. Conf. Texel Island 1994, Prog. Math. 129, 483-509 (1995; Zbl 0860.14024)].
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14C22
Mathematics Subject Classification ID: 14G15
zbMATH DE Number: 1121643
zbMATH Keywords: moduli scheme of stable curves
zbMATH Keywords: characteristic \(p\)
zbMATH Keywords: Néron-Severi group
reviewed by: A. Del Centina
MaRDI profile type: Publication
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full work available at URL: s0022-4049(96)00118-1
OpenAlex ID: W2000705284
Wikidata QID: Q127216913
description: scientific article; zbMATH DE number 1121643