## The Michigan Mathematical Journal

### Veronese quotient models of ̅M0,n and conformal blocks

#### Article information

Source
Michigan Math. J. Volume 62, Issue 4 (2013), 721-751.

Dates
First available in Project Euclid: 16 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1387226162

Digital Object Identifier
doi:10.1307/mmj/1387226162

Mathematical Reviews number (MathSciNet)
MR3160539

Zentralblatt MATH identifier
1287.14011

#### Citation

Gibney, Angela; Jensen, David; Moon, Han-Bom; Swinarski, David. Veronese quotient models of ̅M 0,n and conformal blocks. Michigan Math. J. 62 (2013), no. 4, 721--751. doi:10.1307/mmj/1387226162. https://projecteuclid.org/euclid.mmj/1387226162.

#### References

• V. Alexeev, A. Gibney, and D. Swinarski, Higher level conformal blocks on $\overline{\text{\rm M}}_{0,n}$ from ${\frak lcs}{\frak lcl}_2,$ Proc. Edinburgh Math. Soc. (2) (to appear).
• V. Alexeev and D. Swinarski, Nef Divisors on $\vphantom{\bar t}\overline{\text{\rm M}}_{0,n}$ from GIT, Geometry and arithmetic, pp. 1–21, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2012.
• M. Arap, A. Gibney, J. Stankewicz, and D. Swinarski, ${\frak lcs}{\frak lcl}_n$ level 1 conformal block divisors on $\overline{\text{\rm M}}_{0,n},$ Int. Math. Res. Not. 7 (2012), 1634–1680.
• M. Boggi, Compactifications of configurations of points on $P^{1}$ and quadratic transformations of projective space, Indag. Math. (N.S.) 10 (1999), 191–202.
• I. Coskun, J. Harris, and J. Starr, The effective cone of the Kontsevich moduli space, Canad. Math. Bull. 51 (2008), 519–534.
• N. Fakhruddin, Chern classes of conformal blocks, Compact moduli spaces and vector bundles (Athens, GA, 2010), Contemp. Math., 564, pp. 145–176, Amer. Math. Soc., Providence, RI, 2012.
• M. Fedorchuk, Cyclic covering morphisms on $\overline{\text{\rm M}}_{0,n},$ preprint, 2011, arxiv.org/abs/1105.0655.
• W. Fulton and R. Pandharipande, Notes on stable maps and quantum cohomology, Algebraic geometry (Santa Cruz, 1995), Proc. Sympos. Pure Math., 62, pp. 45–96, Amer. Math. Soc., Providence, RI, 1997.
• N. Giansiracusa, Conformal blocks and rational normal curves, J. of Algebraic Geom. (to appear).
• N. Giansiracusa and A. Gibney, The cone of type A, level 1 conformal block divisors, Adv. Math. 231 (2012), 798–814.
• N. Giansiracusa, D. Jensen, and H.-B. Moon, GIT compactifications of $\overline{\text{\rm M}}_{0,n}$ and flips, preprint, 2011, arxiv.org/abs/1112.0232.
• N. Giansiracusa and M. Simpson, GIT compactifications of $\overline{\text{\rm M}}_{0,n}$ from conics, Int. Math. Res. Not. 14 (2011), 3315–3334.
• B. Hassett, Moduli spaces of weighted pointed stable curves, Adv. Math. 173 (2003), 316–352.
• J. E. Humphreys, Introduction to Lie algebras and representation theory, Grad. Texts in Math., 9, Springer-Verlag, New York, 1978.
• M. M. Kapranov, Chow quotients of Grassmannians. I, Adv. Soviet Math., 16, pp. 29–110, Amer. Math. Soc., Providence, RI, 1993.
• –––, Veronese curves and Grothendieck–Knudsen moduli space $\overline{\text{\rm M}}_{0,n},$ J. Algebraic Geom. 2 (1993), 239–262.
• S. Keel, Basepoint freeness for nef and big line bundles in positive characteristic, Ann. of Math. (2) 149 (1999), 253–286.
• S. Keel and J. McKernan, Contractible extremal rays on $\overline{\text{\rm M}}_{0,n},$ preprint, 1996, arxiv.org/abs/alg-geom/9607009.
• A. Losev and Y. Manin, New moduli spaces of pointed curves and pencils of flat connections, Michigan Math. J. 48 (2000), 443–472.
• D. Mumford, J. Fogarty, and F. Kirwan, Geometric invariant theory, Ergeb. Math. Grenzgeb. (2), 34, Springer-Verlag, Berlin, 1994.
• J. Rasmussen and M. A. Walton, Fusion multiplicities as polytope volumes: N-point and higher-genus $\text{\rm su}(2)$ fusion, Nuclear Phys. B 620 (2002), 537–550.
• M. Simpson, On log canonical models of the moduli space of stable pointed genus zero curves, Ph.D. thesis, Rice Univ., 2008.
• D. Smyth, Towards a classification of modular compactifications of the moduli space of curves, preprint, 2009, arxiv.org/abs/0902.3690.
• D. Swinarski, ConfBlocks: A Macaulay 2 package for computing conformal blocks divisors, ver. 1.0, 2010, $\langle$http://www.math.uiuc.edu/Macaulay2$\rangle.$
• A. Tsuchiya, K. Ueno, and Y. Yamada, Conformal field theory on universal family of stable curves with gauge symmetries, Integrable systems in quantum field theory and statistical mechanics, Adv. Stud. Pure Math., 19, pp. 459–566, Academic Press, Boston, 1989.
• K. Ueno, Conformal field theory with gauge symmetry, Fields Inst. Monogr., 24, Amer. Math. Soc., Providence, RI, 2008.