Abstract
We prove that the moduli variety of curves of genus 3 is rational.
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E. Arbarello andE. Sernesi,The equation of a plane curve, Duke Math J.,46 (1979), 469–485.
F. A. Bogomolov andP. I. Katsylo,Rationality of Some Quotient Varieties, Matem. Sb.168 (1985), 584–589.
M. Chang andZ. Ran,Unirationality of the moduli space of curves of genus 11, 13 (and 12), Invent. Math.76 (1984), 41–54.
A. B. Coble,An application of Moor's cross-ratio group to the solutions of the sextic equation, Trans. Amer. Math. Soc.12 (1911), 311–325.
P. Deligne andD. Mumford,The irreducibility of the space of curves of given genus, Publ. Math. IHES36 (1969), 75–110.
D. Eisenbud andJ. Harris,The Kodaira dimension of the moduli space of curves of genus genus ≥23, Invent Math.90 (1987), 359–387.
R. Hartshorne,Algebraic Geometry, Springer Verlag, Berlin, 1977.
P. I. Katsylo,The rationality of modult spaces of hyperelliptic curves, Math. USSR-Izv.25 (1984), 45–50.
P. I. Katsylo,Rationality of the moduli variety of curves of genus 5, Math. USSR-Sb.72 (1992), 439–445.
P. I. Katsylo,On the birational geometry of the space of ternary quartics, Adv. in Soviet Math.8 (1992), 95–103.
D. Mumford, J. Fogarty andF. Kirwan,Geometric invariant theory, 3rd Edn, Springer Verlag, Berlin, 1994.
H. Popp,Moduli Theory and Classification Theory of Algebraic Varieties, Lect. Notes Math., 620, Springer Verlag, Berlin, 1977.
E. Sernesi,L'unirazionalità della varietà dei moduli delle curvi di genere dodici, An. Sc. Norm. Sup.-Pisa (IV)VIII (1981), 405–439.
N. I. Shepherd-Barron,The rationality of certain spaces associated to trigonal curves, Algebraic Geometry: Bowdoin (1985).
N. I. Shepherd-Barron,Invariant theory for S 5 and the rationality of M 6 Comp. Math.70 (1989), 13–25.
J. Weyman,The equations of strata for binary forms, J. Algebra122 (1989), 244–249.
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Research supported by the Max-Planck-Institut für Mathematik (Bonn, Germany) and Grant N MQZ000 of the International Science Foundation.
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Katsylo, P. Rationality of the moduli variety of curves of genus 3. Commentarii Mathematici Helvetici 71, 507–524 (1996). https://doi.org/10.1007/BF02566434
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DOI: https://doi.org/10.1007/BF02566434