Open Access
October, 2012 Compactified moduli spaces of rational curves in projective homogeneous varieties
Kiryong CHUNG, Jaehyun HONG, Young-Hoon KIEM
J. Math. Soc. Japan 64(4): 1211-1248 (October, 2012). DOI: 10.2969/jmsj/06441211


The space of smooth rational curves of degree $d$ in a projective variety $X$ has compactifications by taking closures in the Hilbert scheme, the moduli space of stable sheaves or the moduli space of stable maps respectively. In this paper we compare these compactifications by explicit blow-ups and -downs when $X$ is a projective homogeneous variety and $d\leq 3$. Using the comparison result, we calculate the Betti numbers of the compactifications when $X$ is a Grassmannian variety.


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Kiryong CHUNG. Jaehyun HONG. Young-Hoon KIEM. "Compactified moduli spaces of rational curves in projective homogeneous varieties." J. Math. Soc. Japan 64 (4) 1211 - 1248, October, 2012.


Published: October, 2012
First available in Project Euclid: 29 October 2012

zbMATH: 1282.14026
MathSciNet: MR2998922
Digital Object Identifier: 10.2969/jmsj/06441211

Primary: 14E30
Secondary: 14D22 , 14F45

Keywords: Betti number , birational morphism , moduli space , projective homogeneous variety

Rights: Copyright © 2012 Mathematical Society of Japan

Vol.64 • No. 4 • October, 2012
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