Illinois Journal of Mathematics

An elementary {GIT} construction of the moduli space of stable maps

Adam E. Parker

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Abstract

This paper provides an elementary construction of the moduli space of stable maps $\overline{M}_{0,0}(\mathbb{P}^r,d)$ as a sequence of "weighted blow-ups along regular embeddings" of a projective variety. This is a corollary to a more general GIT construction of $\overline{M}_{0,n}(\mathbb{P}^r,d)$ that places stable maps, the Fulton-MacPherson space $\mathbb{P}^1[n]$, and curves $\overline{M}_{0,n}$ into a single context.

Article information

Source
Illinois J. Math., Volume 51, Number 3 (2007), 1003-1025.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258131115

Digital Object Identifier
doi:10.1215/ijm/1258131115

Mathematical Reviews number (MathSciNet)
MR2379735

Zentralblatt MATH identifier
1166.14006

Subjects
Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
Secondary: 14H10: Families, moduli (algebraic) 14L24: Geometric invariant theory [See also 13A50]

Citation

Parker, Adam E. An elementary {GIT} construction of the moduli space of stable maps. Illinois J. Math. 51 (2007), no. 3, 1003--1025. doi:10.1215/ijm/1258131115. https://projecteuclid.org/euclid.ijm/1258131115


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