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Stable base locus decompositions of Kontsevich moduli spaces. (English) Zbl 1200.14050
In this paper, the authors study the birational geometry of the Kontsevich space of genus \(0\) unmarked stable maps to Grassmannians \(\overline M_{0,0}(\mathbb G(k, n), d)\). The effective cone is decomposed into chambers according to the stable base locus of the linear series, and the \(8\) chambers for degree \(d=2\) and the \(22\) chambers for degree \(d=3\) are explicitly found. The birational models arising from each chamber in the decomposition are also found, and given modular interpretation in most cases.

14H10 Families, moduli of curves (algebraic)
14E05 Rational and birational maps
14D20 Algebraic moduli problems, moduli of vector bundles
Full Text: DOI arXiv
[1] C. Birkar, P. Cascini, C. D. Hacon, and J. McKernan, The existence of minimal models for varieties of log-general type, J. Amer. Math. Soc. 23 (2010), 405–468. · Zbl 1210.14019 · doi:10.1090/S0894-0347-09-00649-3
[2] D. Chen, Mori’s program for the Kontsevich moduli space \(\overline\mathcal M_0\20(\mathbb P^3,3),\) Int. Math. Res. Not. 2008, article ID rnn067. · Zbl 1147.14009 · doi:10.1093/imrn/rnn067
[3] D. Chen and I. Coskun, with an appendix by C. Crissman, Towards Mori’s program for the moduli space of stable maps, Amer. J. Math. (to appear). · Zbl 1256.14013
[4] I. Coskun, J. Harris, and J. Starr, The effective cone of the Kontsevich moduli spaces, Canad. Math. Bull. 51 (2008), 519–534. · Zbl 1213.14022 · doi:10.4153/CMB-2008-052-5
[5] ——, The ample cone of the Kontsevich moduli space, Canad. J. Math. 61 (2009), 109–123. · Zbl 1206.14050 · doi:10.4153/CJM-2009-005-8
[6] I. Coskun and J. Starr, Divisors on the space of maps to Grassmannians, Int. Math. Res. Not. 2006, article ID 35273. · Zbl 1117.14028 · doi:10.1155/IMRN/2006/35273
[7] J. de Jong and J. Starr, Divisor classes and the virtual canonical bundle for genus zero maps,
[8] L. Ein, R. Lazarsfeld, M. Mustaţǎ, M. Nakamaye, and M. Popa, Asymptotic invariants of base loci, Ann. Inst. Fourier (Grenoble) 56 (2006), 1701–1734. · Zbl 1127.14010 · doi:10.5802/aif.2225 · numdam:AIF_2006__56_6_1701_0 · eudml:10189
[9] ——, Restricted volumes and base loci of linear series, Amer. J. Math. 131 (2009), 607–651. · Zbl 1179.14006 · doi:10.1353/ajm.0.0054 · muse.jhu.edu
[10] A. Mustaţǎ and M. A. Mustaţǎ, Intermediate moduli spaces of stable maps, Invent. Math. 167 (2007), 47–90. · Zbl 1111.14018 · doi:10.1007/s00222-006-0006-1
[11] D. Oprea, Divisors on the moduli space of stable maps to flag varieties and reconstruction, J. Reine Angew. Math. 586 (2005), 169–205. · Zbl 1089.14004 · doi:10.1515/crll.2005.2005.586.169
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