REFERENCES
- Arbarello , [Arbarello et al. 85] Enrico , Cornalba , Maurizio , Griffiths , Phillip and Harris , Joe . 1985 . Geometry of Algebraic Curves. Vol. I, Grundlehren der Mathematischen Wissenschaften 267 , New York : Springer .
- Baldwin , [Baldwin and Swinarski 08] Elizabeth and Swinarski , David . 2008 . “A Geometric Invariant Theory Construction of Moduli Spaces of Stable Maps . Int. Math. Res. Pap. IMRP , 1 Art. ID rpn 004, 104. Available at arXiv:0706.1381v3
- Bayer , [Bayer 82] Davd . 1982 . The Division Algorithm and the Hilbert Scheme.” PhD thesis , Harvard University .
- Bayer , [Bayer and Eisenbud 85] Dave and Eisenbud , David . 1995 . “Ribbons and Their Canonical Embeddings . Trans. Amer. Math. Soc. , 347 : 719 – 756 .
- Bayer , [Bayer and Morrison 88] David and Morrison , Ian . 1988 . “Standard Bases and Geometric Invariant Theory. I. Initial Ideals and State Polytopes . J. Symbolic Comput. , 6 : 209 – 217 .
- Bosma , [Bosma et al. 97] Wieb , Cannon , John and Playoust , Catherine . 1997 . “The Magma Algebra System. I. The User Language . J. Symbolic Comput. , 24 : 235 – 265 .
- Breuer , [Breuer 00] Thomas . 2000 . Characters and Automorphism Groups of Compact Riemann Surfaces, London Mathematical Society Lecture Note Series 280 , Cambridge, UK : Cambridge University Press .
- Dolgachev , [Dolgachev and Hu 98] Igor V. and Hu , Yi . 1988 . Variation of Geometric Invariant Theory Quotients . Inst. Hautes Études Sci. Publ. Math. , 87 : 5 – 56 .
- Eisenbud , [Eisenbud 80] David . 1980 . “Transcanonical Embeddings of Hyperelliptic Curves . J. Pure Appl. Algebra , 19 : 77 – 83 .
- Fogarty , [Fogarty et al. 94] John , Kirwan , Frances and Mumford , David . 1994 . Geometric Invariant Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (2) 34 , Berlin : Springer .
- Gawrilow , [Gawrilow and Joswig 00] Ewgenij and Joswig , Michael . 2000 . “Polymake: A Framework for Analyzing Convex Polytopes ” . In Polytopes—Combinatorics and Computation, Oberwolfach 1997, DMV Sem. 29 , 43 – 73 . Basel : Birkhäuser .
- Gibney , [Gibney et al. 02] Angela , Keel , Seán and Morrison , Ian . 2002 . “Towards the Ample Cone of . J. Amer. Math. Soc. , 15 : 273 – 294 . (electronic)
- Gieseker , [Gieseker 77] David . 1977 . “Global Moduli for Surfaces of General Type . Invent. Math. , 43 : 233 – 282 .
- Gieseker , [Gieseker 82] David . 1982 . Lectures on Moduli of Curves, Tata Institute of Fundamental Research Lectures on Mathematics and Physics 69 , Bombay : Tata Institute of Fundamental Research .
- Gieseker , [Gieseker 83] David . 1983 . “Geometric Invariant Theory and Applications to Moduli Problems ” . In Invariant Theory , Edited by: Gherardelli , Francesco . 45 – 73 . New York : Springer . Lecture Notes in Mathematics 996
- Gotzmann , [Gotzmann 78] Gerd . 1978 . “Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes . Math. Z. , 158 : 61 – 70 .
- Haiman , [Haiman and Sturmfels 04] Mark and Sturmfels , Bernd . 2004 . “Multigraded Hilbert Schemes . J. Algebraic Geom. , 13 : 735 – 769 .
- Harris , [Harris 95] Joe . 1995 . Algebraic Geometry: A First Course, Graduate Texts in Mathematics, 133 , New York : Springer .
- Hassett , [Hassett and Hyeon 08] Brendan and Hyeon , Donghoon . 2008 . “Log Minimal Model Program for the Moduli Space of Stable Curves: The First Flip . arXiv:0806.3444v1
- Hassett , [Hassett and Hyeon 09] Brendan and Hyeon , Donghoon . 2009 . “Log canonical Models for the Moduli Space of Stable Curves: First Divisorial Contraction” . Trans. Amer. Math. Soc. , 361 : 4471 – 4489 .
- Hassett , [Hassett et al. 10] Brendan , Hyeon , Donghoon and Lee , Yongnam . 2010 . “Stability Computation via Gröbner Bases . J. Korean Math. Soc. , 47 : 41 – 62 .
- Hyeon , [Hyeon 10] Donghoon . 2010 . “An Outline of the Log Minimal Model Program for the Moduli Space of Curves” . arXiv:math/1006.1094
- Hyeon , [Hyeon and Lee 10] Donghoon and Lee , Yongnam . 2010 . Log Minimal Model Program for the Moduli Space of Stable Curves of Genus Three . Math. Res. Lett , 17 : 625 – 636 .
- Kapranov , [Kapranov et al. 92] M. M. , Sturmfels , B. and Zelevinsky , A. V. 1992 . “Chow Polytopes and General Resultants” . Duke Math. J. , 67 : 189 – 218 .
- Kempf , [Kempf 78] George R. 1978 . “Instability in Invariant Theory . Ann. of Math. (2) , 108 : 299 – 316 .
- Maclachlan , [Maclachlan 65] C. 1965 . Abelian Groups of Automorphisms of Compact Riemann Surfaces . Proc. London Math. Soc. (3) , 15 : 699 – 712 .
- Ian , [Morrison 08] Morrison . “GIT Constructions of Moduli Spaces of Stable Curves and Maps” . Surveys in differential geometry. Vol. XIV. Geometry of Riemann surfaces and their moduli spaces , Surv. Differ. Geom., 14, Int. Press, Somerville, MA, 2009, 315–369, 2655332
- Morrison , [Morrison and Swinarski 09] Ian and Swinarski , David . “Annotated Code Samples to Accompany ‘Gröbner Techniques for Low-Degree Hilbert Stability.’,” . Available online (http://www.math.uga.edu/~davids/ gs/codesamples.pdf)
- Mumford , [Mumford 77] David . 1977 . Stability of Projective Varieties, Monographie de l’Enseignement Mathématique 24 , Geneva : L’Enseignement Mathématique .
- Rousseau , [Rousseau 78] Guy . 1978 . “Immeubles sphériques et théorie des invariants” . C. R. Acad. Sci. Paris Sér. A-B , 286 : A247 – A250 .
- Smyth , [Smyth 08] David Ishii . 2008 . “Modular Compactifications of M 1,n ” . arXiv:0808.0177
- Smyth , [Smyth 09] David Ishii . 2009 . “Towards a Classification of Modular Compactifications of the Moduli Space of Curves” . arXiv:0902.3690
- Stevens , [Stevens 03] Jan . 2003 . Deformations of Singularities, Lecture Notes in Mathematics 1811 , Berlin : Springer .
- Sturmfels , [Sturmfels 96] Bernd . 1996 . Gröbner Bases and Convex Polytopes, University Lecture Series 8 , Providence : American Mathematical Society .
- Thaddeus , [Thaddeus 96] Michael . 1996 . “Geometric Invariant Theory and Flips” . J. Amer. Math. Soc. , 9 : 691 – 723 .
- Wiman , [Wiman 95] Anders . 1895 . Über die Doppelcurve auf den geradlinigen Flächen . Acta Math. , 19 : 63 – 71 .
SOFTWARE PACKAGES REFERENCED
- Franz , [Franz 06] Matthias . 2006 . “Convex: A Maple Package for Convex Geometry” . Available at http://www. math.uwo.ca/mfranz/convex. Version 1.1.2
- [GAP Group 08] The GAP Group . 2008 . GAP: Groups, Algorithms, and Programming: A System for Computational Discrete Algebra . Available at http://www.gap-system.org. Version 4.4.11
- Jensen , [Jensen 08] Anders . 2008 . gfan: A Software Package for Computing Gröbner Fans and Tropical Varieties . Available at http://www.math.tu-berlin.de/~jensen/software/gfan/gfan.html. Version 0.3
- Grayson , [Grayson and Stillman 08] Dan and Stillman , Mike . 2008 . “Macaulay 2: A Software System for Research in Algebraic Geometry . Available at http://www.math.uiuc.edu/Macaulay2/. Version 1.1
- 2008 . [Magma 08] Computational Algebra Research Group, School of Mathematics and Statistics, University of Sydney . “MAGMA Computational Algebra System.” Available at http://magma.maths.usyd.edu.au/magma/. Version 2.15-1
- Gawrilow , [Gawrilow and Joswig 07] Ewgenij and Joswig , Michael . 2007 . “polymake: A Framework for Analyzing Convex Polytopes . Available at http://www.math.tu-berlin.de/polymake/. Version 2.3