The effective cone of the Kontsevich moduli space

Izzet Coskun; Joe Harris; Jason Starr

doi:10.4153/CMB-2008-052-5

The effective cone of the Kontsevich moduli space

Izzet Coskun
, Joe Harris
, Jason Starr

Mathematics

Stony Brook University

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

18 Scopus citations

Abstract

In this paper we prove that the cone of effective divisors on the Kontsevich moduli spaces of stable maps, M̄ _0,0(ℙ^r, d), stabilize when r ≥ d. We give a complete characterization of the effective divisors on M̄ _0,0(ℙ^d, d). They are non-negative linear combinations of boundary divisors and the divisor of maps with degenerate image.

Original language	English
Pages (from-to)	519-534
Number of pages	16
Journal	Canadian Mathematical Bulletin
Volume	51
Issue number	4
DOIs	https://doi.org/10.4153/CMB-2008-052-5
State	Published - Dec 2008

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

abstract = "In this paper we prove that the cone of effective divisors on the Kontsevich moduli spaces of stable maps, {\=M} 0,0(ℙr, d), stabilize when r ≥ d. We give a complete characterization of the effective divisors on {\=M} 0,0(ℙd, d). They are non-negative linear combinations of boundary divisors and the divisor of maps with degenerate image.",

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

year = "2008",

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doi = "10.4153/CMB-2008-052-5",

language = "English",

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T1 - The effective cone of the Kontsevich moduli space

AU - Coskun, Izzet

AU - Harris, Joe

AU - Starr, Jason

PY - 2008/12

Y1 - 2008/12

N2 - In this paper we prove that the cone of effective divisors on the Kontsevich moduli spaces of stable maps, M̄ 0,0(ℙr, d), stabilize when r ≥ d. We give a complete characterization of the effective divisors on M̄ 0,0(ℙd, d). They are non-negative linear combinations of boundary divisors and the divisor of maps with degenerate image.

AB - In this paper we prove that the cone of effective divisors on the Kontsevich moduli spaces of stable maps, M̄ 0,0(ℙr, d), stabilize when r ≥ d. We give a complete characterization of the effective divisors on M̄ 0,0(ℙd, d). They are non-negative linear combinations of boundary divisors and the divisor of maps with degenerate image.

UR - https://www.scopus.com/pages/publications/57649101980

U2 - 10.4153/CMB-2008-052-5

DO - 10.4153/CMB-2008-052-5

M3 - Article

SN - 0008-4395

VL - 51

SP - 519

EP - 534

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

IS - 4

ER -

The effective cone of the Kontsevich moduli space

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