An Outline of the Log Minimal Model Program for the Moduli Space of Curves

References

• [Alper et al. 13] J. Alper, M. Fedorchuk, S. David, and F. van der Wyck. “Log Minimal Model Program for the Moduli Space of Stable Curves: The Second Flip.” 2013. arXiv:1308.1148 [math.AG].
   Google Scholar
• [Alper et al. 10] J. Alper, M. Fedorchuk, and D. I. Smyth. “Singularities with Gm-Action and the Log Minimal Model Program for .” to appear in the J. Reine. Angew. Math (2010). arXiv:1010.3751v1 [math.AG].
   Google Scholar
• [Alper et al. 12] J. Alper and D. Hyeon. “GIT Constructions of Log Canonical Models of .” In Compact Moduli Spaces and Vector Bundles, volume 564 of Contemp. Math., edited by V. Alexeev, A. Gibney, E. Izadi, J. Kollár, and E. Looijenga, Providence, RI: Amer. Math. Soc., 2012.
   Google Scholar
• [Avritzer and Lange 02] D. Avritzer and H. Lange. “The Moduli Spaces of Hyperelliptic Curves and Binary Forms.” Math. Z. 242:4 (2002), 615–632.
   Web of Science ®Google Scholar
• [Alexeev and Swinarski 12] V. Alexeev and D. Swinarski. “Nef Divisors on From GIT.” In Geometry and Arithmetic, edited by C. Faber, G. Farkas, and R. de Jong, EMS Ser. Congr. Rep., (pp. 1–21). Zürich: Eur. Math. Soc., 2012.
   Google Scholar
• [Birkar et al. 10] C. Birkar, P. Cascini, C. D. Hacon, and J. McKernan. “Existence of Minimal Models for Varieties of Log General Type.” J. Am. Math. Soc. 23:2 (2010), 405–468.
   Web of Science ®Google Scholar
• [Casalaina-Martin et al. 12] S. Casalaina-Martin, D. Jensen, and R. Laza. “The Geometry of the Ball Quotient Model of the Moduli Space of Genus Four Curves.” In Compact Moduli Spaces and Vector Bundles, volume 564 of Contemp. Math., pp. 107–136. Providence, RI: Amer. Math. Soc., 2012.
   Google Scholar
• [Casalaina-Martin et al. 14] S. Casalaina-Martin, D. Jensen, and R. Laza. “Log Canonical Models and Variation of GIT for Genus Four Canonical Curves.” J. Algebraic Geom. 23:4 (2014), 727–764.
   Web of Science ®Google Scholar
• [Doran and Kirwan 07] B. Doran and F. Kirwan. “Towards Non-Reductive Geometric Invariant Theory.” Pure Appl. Math. Q. 3:1, part 3 (2007), 61–105.
   Web of Science ®Google Scholar
• [Farkas 09] G. Farkas. “The Global Geometry of the Moduli Space of Curves.” In Algebraic geometry—Seattle 2005. Part 1, volume 80 of Proc. Sympos. Pure Math., pp. 125–147. Providence, RI: Amer. Math. Soc., 2009.
   Google Scholar
• [Fedorchuk and Jensen 13] M. Fedorchuk and D. Jensen. “Stability of 2nd Hilbert Points of Canonical Curves.” Int. Math. Res. Not. IMRN 22 (2013), 5270–5287.
   Google Scholar
• [Fedorchuk and Smyth 13] M. Fedorchuk and D. I. Smyth. “Alternate Compactifications of Moduli Spaces of Curves.” In Handbook of moduli. Vol. I, volume 24 of Adv. Lect. Math. (ALM), edited by G. Farkas and I. Morrison, pp. 331–413. Somerville, MA: Int. Press, 2013.
   Google Scholar
• [Gibney 09] A. Gibney. “Numerical Criteria for Divisors on to be Ample.” Compos. Math. 145:5 (2009), 1227–1248.
   Web of Science ®Google Scholar
• [Gibney et al. 02] A. Gibney, S. Keel, I. Morrison. “Towards the Ample Cone of .” J. Am. Math. Soc. 15:2 (2002), 273–294 ( electronic).
   Web of Science ®Google Scholar
• [Gotzmann 78] G. Gotzmann. “Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes.” Math. Z. 158:1 (1978), 61–70.
   Web of Science ®Google Scholar
• [Hassett 00] B. Hassett. “Local Stable Reduction of Plane Curve Singularities.” J. Reine Angew. Math., 520 (2000), 169–194.
   Web of Science ®Google Scholar
• [Hassett 05] B. Hassett. “Classical and Minimal Models of the Moduli Space of Curves of Genus Two.” In Geometric Methods in Algebra and Number Theory, volume 235 of Progress in Mathematics, pp. 160–192. Boston: Birkhäuser, 2005.
   Google Scholar
• [Hassett and Hyeon 09] B. Hassett and D. Hyeon. “Log Canonical Models for the Moduli Space of Curves: The First Divisorial Contraction.” Trans. Am. Math. Soc. 361:8 (2009), 4471–4489.
   Web of Science ®Google Scholar
• [Hassett and Hyeon 13] B. Hassett and D. Hyeon. “Log Minimal Model Program for the Moduli Space of Stable Curves: The First Flip.” Ann. Math. (2). 177:3 (2013), 911–968.
   Web of Science ®Google Scholar
• [Hassett et al. 10] B. Hassett, D. Hyeon, and Y. Lee. “Stability Computation via Gröbner Basis.” J. Korean Math. Soc. 47:1 (2010), 41–62.
   Web of Science ®Google Scholar
• [Hyeon and Lee 07] D. Hyeon and Y. Lee. “Stability of Tri-Canonical Curves of Genus Two.” Math. Ann. 337:2 (2007), 479–488.
   Web of Science ®Google Scholar
• [Hyeon and Lee 10a] D. Hyeon and Y. Lee. “Log Minimal Model Program for the Moduli Space of Stable Curves of Genus Three.” Math. Res. Lett. 17:4 (2010), 625–636.
   Web of Science ®Google Scholar
• [Hyeon and Lee 10b] D. Hyeon and Y. Lee. “A New Look at the Moduli Space of Stable Hyperelliptic Curves.” Math. Z. 264:2 (2010), 317–326.
   Web of Science ®Google Scholar
• [Hyeon and Morrison 10] D. Hyeon and I. Morrison. “Stability of Tails and 4-Canonical Models.” Math. Res. Lett. 17:4 (2010), 721–729.
   Web of Science ®Google Scholar
• [Keel and McKernan 96] S. Keel and J. McKernan. “Contractible Extremal Rays on .” 1996. arXiv:alg-geom/9607009v1.
   Google Scholar
• [Kollár and Mori 98] J. Kollár and S. Mori. Birational Geometry of Algebraic Varieties, volume 134 of Cambridge Tracts in Mathematics. Cambridge: Cambridge University Press, 1998. With the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original.
   Google Scholar
• [Kiem and Moon 11] Y.-H. Kiem and H.-B. Moon. “Moduli Spaces of Weighted Pointed Stable Rational Curves via GIT.” Osaka J. Math. 48:4 (2011), 1115–1140.
   Web of Science ®Google Scholar
• [Mumford et al. 94] D. Mumford, J. Fogarty, and F. Kirwan. Geometric Invariant Theory, volume 34 of Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)]. Third edition, Berlin: Springer-Verlag, 1994.
   Google Scholar
• [Mumford 77] D. Mumford. “Stability of Projective Varieties.” Enseignement Math. (2). 23:1–2 (1977), 39–110.
   Google Scholar