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The Effective Cone of the Kontsevich Moduli Space

Published online by Cambridge University Press:  20 November 2018

Izzet Coskun ,
Joe Harris  and
Jason Starr
Izzet Coskun
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607. e-mail: coskun@math.uic.edu
Joe Harris
Affiliation:
Department of Mathematics, Stony Brook University, Stony Brook, NY 11794. e-mail: jstarr@math.sunysb.edu
Jason Starr
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA 02138. e-mail: harris@math.harvard.edu
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Abstract

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In this paper we prove that the cone of effective divisors on the Kontsevich moduli spaces of stable maps, ${{\overline{M}}_{0,0}}\left( {{\mathbb{P}}^{r}},\,d \right)$ , stabilize when $r\,\ge \,d$. We give a complete characterization of the effective divisors on ${{\overline{M}}_{0,0}}\left( {{\mathbb{P}}^{d}},\,d \right)$ . They are non-negative linear combinations of boundary divisors and the divisor of maps with degenerate image.

Keywords

14D2014E9914H10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 4 , 01 December 2008 , pp. 519 - 534
Copyright
Copyright © Canadian Mathematical Society 2008

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