The ample cone of the Kontsevich moduli space

Izzet Coskun; Joe Harris; Jason Starr

doi:10.4153/CJM-2009-005-8

The ample cone of the Kontsevich moduli space

Izzet Coskun
, Joe Harris
, Jason Starr

Mathematics

Stony Brook University

University of Illinois at Chicago
Harvard University

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We produce ample (resp. NEF, eventually free) divisors in the Kontsevich space M ₀, _n(P ^r, d) of n-pointed, genus 0, stable maps to P ^r, given such divisors in M̄; _0+d We prove that this produces all ample (resp. NEF, eventually free) divisors in M̄ _o, _n(P ^r, d). As a consequence, we construct a contraction of the boundary Δ _k, _d- _k m M̄ ₀, 3 ₀(P ^r, d), analogous to a contraction of the boundary Δ _k, _n- _k in M̄ ₀, _n first constructed by Keel and McKernan.

Original language	English
Pages (from-to)	109-123
Number of pages	15
Journal	Canadian Journal of Mathematics
Volume	61
Issue number	1
DOIs	https://doi.org/10.4153/CJM-2009-005-8
State	Published - Feb 2009

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title = "The ample cone of the Kontsevich moduli space",

abstract = "We produce ample (resp. NEF, eventually free) divisors in the Kontsevich space M 0, n(P r, d) of n-pointed, genus 0, stable maps to P r, given such divisors in {\=M}; 0+d We prove that this produces all ample (resp. NEF, eventually free) divisors in {\=M} o, n(P r, d). As a consequence, we construct a contraction of the boundary Δ k, d- k m {\=M} 0, 3 0(P r, d), analogous to a contraction of the boundary Δ k, n- k in {\=M} 0, n first constructed by Keel and McKernan.",

author = "Izzet Coskun and Joe Harris and Jason Starr",

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AU - Coskun, Izzet

AU - Harris, Joe

AU - Starr, Jason

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N2 - We produce ample (resp. NEF, eventually free) divisors in the Kontsevich space M 0, n(P r, d) of n-pointed, genus 0, stable maps to P r, given such divisors in M̄; 0+d We prove that this produces all ample (resp. NEF, eventually free) divisors in M̄ o, n(P r, d). As a consequence, we construct a contraction of the boundary Δ k, d- k m M̄ 0, 3 0(P r, d), analogous to a contraction of the boundary Δ k, n- k in M̄ 0, n first constructed by Keel and McKernan.

AB - We produce ample (resp. NEF, eventually free) divisors in the Kontsevich space M 0, n(P r, d) of n-pointed, genus 0, stable maps to P r, given such divisors in M̄; 0+d We prove that this produces all ample (resp. NEF, eventually free) divisors in M̄ o, n(P r, d). As a consequence, we construct a contraction of the boundary Δ k, d- k m M̄ 0, 3 0(P r, d), analogous to a contraction of the boundary Δ k, n- k in M̄ 0, n first constructed by Keel and McKernan.

UR - https://www.scopus.com/pages/publications/60849085169

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DO - 10.4153/CJM-2009-005-8

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SP - 109

EP - 123

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

IS - 1

ER -

The ample cone of the Kontsevich moduli space

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