Ample divisors on moduli spaces of pointed rational curves
Authors:
Maksym Fedorchuk and David Ishii Smyth
Journal:
J. Algebraic Geom. 20 (2011), 599-629
DOI:
https://doi.org/10.1090/S1056-3911-2011-00547-X
Published electronically:
January 25, 2011
MathSciNet review:
2819671
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Abstract |
References |
Additional Information
Abstract: We introduce a new technique for proving positivity of certain divisor classes on $\overline {M}_{0,n}$ and its weighted variants $\overline {M}_{0,\mathcal {A}}$. Our methods give a complete description of the models arising in the Hassett’s log minimal model program for $\overline {M}_{0,n}$.
References
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- Valery Alexeev and David Swinarski, Nef divisors on $\overline {M}_{0,n}$ from GIT, arXiv:0812.0778, 2008.
- Joe Harris and Ian Morrison, Moduli of curves, Graduate Texts in Mathematics, vol. 187, Springer-Verlag, New York, 1998. MR 1631825
- Brendan Hassett, Moduli spaces of weighted pointed stable curves, Adv. Math. 173 (2003), no. 2, 316–352. MR 1957831, DOI https://doi.org/10.1016/S0001-8708%2802%2900058-0
- Brendan Hassett, Classical and minimal models of the moduli space of curves of genus two, Geometric methods in algebra and number theory, Progr. Math., vol. 235, Birkhäuser Boston, Boston, MA, 2005, pp. 169–192. MR 2166084, DOI https://doi.org/10.1007/0-8176-4417-2_8
- Sean Keel and James McKernan, Contractible extremal rays on $\overline {M}_{0,n}$, arXiv:9607.009, 1996.
- János Kollár, Projectivity of complete moduli, J. Differential Geom. 32 (1990), no. 1, 235–268. MR 1064874
- János Kollár, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 32, Springer-Verlag, Berlin, 1996. MR 1440180
- Matthew Simpson, On log canonical models of the moduli space of stable pointed genus zero curves, Ph.D. thesis, Rice University, 2008.
References
- Valery Alexeev and G. Michael Guy, Moduli of weighted stable maps and their gravitational descendants, J. Inst. Math. Jussieu 7 (2008), no. 3, 425–456. MR 2427420 (2009f:14112)
- Valery Alexeev and David Swinarski, Nef divisors on $\overline {M}_{0,n}$ from GIT, arXiv:0812.0778, 2008.
- Joe Harris and Ian Morrison, Moduli of curves, Graduate Texts in Mathematics, vol. 187, Springer-Verlag, New York, 1998. MR 1631825 (99g:14031)
- Brendan Hassett, Moduli spaces of weighted pointed stable curves, Adv. Math. 173 (2003), no. 2, 316–352. MR 1957831 (2004b:14040)
- ---, Classical and minimal models of the moduli space of curves of genus two, Geometric methods in algebra and number theory, Progr. Math., vol. 235, Birkhäuser Boston, Boston, MA, 2005, pp. 169–192. MR 2166084 (2006g:14047)
- Sean Keel and James McKernan, Contractible extremal rays on $\overline {M}_{0,n}$, arXiv:9607.009, 1996.
- János Kollár, Projectivity of complete moduli, J. Differential Geom. 32 (1990), no. 1, 235–268. MR 1064874 (92e:14008)
- ---, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 32, Springer-Verlag, Berlin, 1996. MR 1440180 (98c:14001)
- Matthew Simpson, On log canonical models of the moduli space of stable pointed genus zero curves, Ph.D. thesis, Rice University, 2008.
Additional Information
Maksym Fedorchuk
Affiliation:
Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
MR Author ID:
768613
Email:
mfedorch@math.columbia.edu
David Ishii Smyth
Affiliation:
Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, Massachusetts 02138
MR Author ID:
729731
Email:
dsmyth@math.harvard.edu
Received by editor(s):
December 8, 2008
Received by editor(s) in revised form:
September 25, 2009
Published electronically:
January 25, 2011
Additional Notes:
The second author was partially supported by a Clay Mathematics Institute Liftoff Fellowship during the preparation of this paper.
