Advanced search
Publication Cover
Experimental Mathematics Volume 18, 2009 - Issue 4
Submit an article Journal homepage
36
Views
1
CrossRef citations to date
0
Altmetric
Original Article

Rationality of Moduli Spaces of Plane Curves of Small Degree

Christian Böhning Mathematisches Institut, Courant Research Center for Higher Order Structures, Georg-August-Universität Göttingen, Bunsenstr. 3–5, Göttingen, 37073, Germany
,
Hans-Christian Graf von Bothmer Mathematisches Institut, Courant Research Center for Higher Order Structures, Georg-August-Universität Göttingen, Bunsenstr. 3–5, Göttingen, 37073, Germany
&
Jakob Kröker Mathematisches Institut, Courant Research Center for Higher Order Structures, Georg-August-Universität Göttingen, Bunsenstr. 3–5, Göttingen, 37073, Germany
Pages 499-508 | Published online: 30 Jan 2011

  • F. A. Bogomolov. "Holomorphic Tensors and Vector Bundles on Projective Varieties." Math. USSR Izvestija 13:3 (1979), 499–555.
  • F. Bogomolov. "Stable Rationality of Quotient Varieties by Simply Connected Groups." Mat. Sbornik 130 (1986), 3–17.
  • F. Bogomolov. "Rationality of the Moduli of Hyperelliptic Curves of Arbitrary Genus." In Conf. Alg. Geom., Vancouver 1984, CMS Conf. Proceedings 6, pp. 17–37. Providence: Amer. Math. Soc., 1986. 17–37.
  • F. Bogomolov and P. Katsylo. "Rationality of Some Quotient Varieties." Mat. Sbornik 126 (1985), 584–589.
  • Chr. Böhning and H.-Chr. Graf v. Bothmer. "The Rationality of theModuli Spaces of Plane Curves of Sufficiently Large Degree." arXiv:0804.1503, 2008.
  • Chr. Böhning and H.-Chr. Graf v. Bothmer. "Macaulay2 Scripts to Check the Surjectivity of the Scorza and Octa Maps." Available online ( http:// www.uni-math.gwdg.de/bothmer/rationality
  • Chr. Böhning and H.-Chr. Graf v. Bothmer. "A Clebsch–Gordan Formula for SL3(C) and Applications to Rationality." arXiv:0812.3278, 2008.
  • Chr. Böhning and H.-Chr. Graf v. Bothmer. "Macaulay2 Scripts for 'A Clebsch–Gordan Formula for SL3(C) and Applications to Rationality.' " Available online ( http://www.uni-math.gwdg.de/ bothmer/ClebschGordan
  • Chr. Böhning, H.-Chr. Graf v. Bothmer, and J. Kröker. "Macaulay2 Scripts for 'Rationality of Moduli Spaces of Plane Curves of Small Degree.' " Available online ( http://www.uni-math.gwdg.de/ bothmer/smallDegree
  • V. Chernousov, Ph. Gille, and Z. Reichstein. "Resolving G -Torsors by Abelian Base Extensions." J. Algebra 296 (2006), 561–581.
  • J.-L. Colliot-Thélène and J.-J. Sansuc. "The Rationality Problem for Fields of Invariants under Linear Algebraic Groups (with Special Regards to the Brauer Group)." In Algebraic Groups and Homogeneous Spaces . Mumbai: Tata Inst. Fund. Res. Stud. Math., pp. 113–186, 2007.
  • I. Dolgachev. "Rationality of Fields of Invariants." Proceedings of Symposia in Pure Mathematics 46 (1987), 3–16.
  • J.-G. Dumas, T. Gautier, P. Giorgi, and C. Pernet. "FFLAS-FFPACK Finite Field Linear Algebra Subroutines." Software package available online ( http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/ FFLAS
  • J. H. Grace and W. H. Young. The Algebra of Invariants . Cambridge, UK: Cambridge Univ. Press, 1903 (reprinted by Chelsea, New York, 1965).
  • P. I. Katsylo. "Rationality of Orbit Spaces of Irreducible Representations of SL2." Izv. Akad. Nauk SSSR, Ser. Mat. 47:1 (1983), 26–36 (English translation in Math USSR Izv. 22 (1984), 23–32).
  • P. I. Katsylo. "Rationality of the Moduli Spaces of Hyperelliptic Curves." Izv. Akad. Nauk SSSR Ser. Mat. 48 (1984), 705–710.
  • P. I. Katsylo. "Rationality of Moduli Varieties of Plane Curves of Degree 3k ." Math. USSR Sbornik 64:2 (1989), 375–381.
  • P. I. Katsylo. "Birational Geometry of Moduli Varieties of Vector Bundles over P2." Math. USSR Izvestiya 38:2 (1992), 419–428.
  • P. I. Katsylo. "Rationality of the Moduli Variety of Curves of Genus 5." Math. USSR Sbornik 72:2 (1992), 439–445.
  • P. I. Katsylo. "On the Birational Geometry of the Space of Ternary Quartics." Advances in Soviet Math. 8 (1992), 95–103.
  • P. I. Katsylo. "On the Birational Geometry of (Pn)(m)/ GLn +1." Max-Planck Institut preprint, MPI/94 144, 1994.
  • P. I. Katsylo. "Rationality of the Moduli Variety of Curves of Genus 3." Comment. Math. Helvetici 71 (1996), 507–524.
  • M. Rosenlicht. "Some Basic Theorems on Algebraic Groups." American Journal of Mathematics 78:2 (1956), 401–443.
  • J.-P. Serre. "Espaces fibrés algébriques." Séminaire Claude Chevalley exp. no. 1, 3 (1958), 1–37.
  • N. I. Shepherd-Barron. "The Rationality of Some Moduli Spaces of Plane Curves." Compositio Mathematica 67 (1988), 51–88.
  • N. I. Shepherd-Barron. "Rationality of Moduli Spaces via Invariant Theory." In Topological Methods in Algebraic Transformation Groups (New Brunswick, NJ, 1988), Progr. Math. 80, pp. 153–164. Boston: Birkhäuser, 1989.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.