Geodesic
The rationality of the moduli spaces of~Coble surfaces and of nodal Enriques surfaces
Izvestiya. Mathematics , Tome 77 (2013) no. 3, pp. 509-524.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove the rationality of the coarse moduli spaces of Coble surfaces and of nodal Enriques surfaces over the field of complex numbers. Bibliography: 22 titles.
Keywords: Coble surfaces, rationality problem.
Mots-clés : Enriques surfaces, moduli spaces 
@article{IM2_2013_77_3_a4,
     author = {I. V. Dolgachev and Sh. Kondo},
     title = {The rationality of the moduli spaces {of~Coble} surfaces and of nodal {Enriques} surfaces},
     journal = {Izvestiya. Mathematics },
     pages = {509--524},
     publisher = {mathdoc},
     volume = {77},
     number = {3},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2013_77_3_a4/}
}
TY  - JOUR
AU  - I. V. Dolgachev
AU  - Sh. Kondo
TI  - The rationality of the moduli spaces of~Coble surfaces and of nodal Enriques surfaces
JO  - Izvestiya. Mathematics 
PY  - 2013
SP  - 509
EP  - 524
VL  - 77
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2013_77_3_a4/
LA  - en
ID  - IM2_2013_77_3_a4
ER  - 
%0 Journal Article
%A I. V. Dolgachev
%A Sh. Kondo
%T The rationality of the moduli spaces of~Coble surfaces and of nodal Enriques surfaces
%J Izvestiya. Mathematics 
%D 2013
%P 509-524
%V 77
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2013_77_3_a4/
%G en
%F IM2_2013_77_3_a4
I. V. Dolgachev; Sh. Kondo. The rationality of the moduli spaces of~Coble surfaces and of nodal Enriques surfaces. Izvestiya. Mathematics , Tome 77 (2013) no. 3, pp. 509-524. http://geodesic.mathdoc.fr/item/IM2_2013_77_3_a4/

[1] S. Kondō, “The rationality of the moduli space of Enriques surfaces”, Compositio Math., 91:2 (1994), 159–173 | MR | Zbl

[2] T. Miyata, “Invariants of certain groups. I”, Nagoya Math. J., 41 (1971), 69–73 | MR | Zbl

[3] Moscow Univ. Math. Bull., 37:2 (1982), 27–29 | MR | Zbl

[4] S. Ma, Rationality of the moduli spaces of $2$-elementary $\mathrm{K3}$ surfaces, to appear in J. Algebraic Geom., arXiv: 1110.5110

[5] J. Math. Sci., 81:3 (1996), 2599–2630 | DOI | MR | Zbl

[6] Y. Namikawa, “Periods of Enriques surfaces”, Math. Ann., 270:2 (1985), 201–222 | DOI | MR | Zbl

[7] Soviet Math. Dokl., 30:1 (1984), 282–285 | MR | Zbl

[8] I. V. Dolgachev and D.-Q. Zhang, “Coble rational surfaces”, Amer. J. Math., 123:1 (2001), 79–114 | DOI | MR | Zbl

[9] A. B. Coble, Algebraic geometry and theta functions, Amer. Math. Soc., New York, 1929 | MR | Zbl

[10] S. Cantat and I. Dolgachev, “Rational surfaces with a large group of automorphisms”, J. Amer. Math. Soc., 25:3 (2012), 863–905 | DOI | MR | Zbl

[11] A. Coble, “The ten nodes of the rational sextic and of the Cayley symmetroid”, Amer. J. Math., 41:4 (1919), 243–265 | DOI | MR | Zbl

[12] Math. USSR-Izv., 14:1 (1980), 103–167 | DOI | MR | Zbl | Zbl

[13] Math. USSR-Izv., 5:3 (1971), 547–588 | DOI | MR | Zbl | Zbl

[14] D. R. Morrison and M.-H. Saito, “Cremona transformations and degrees of period maps for $\mathrm{K3}$ surfaces with ordinary double points”, Algebraic geometry (Sendai, Japan 1985), Adv. Stud. Pure Math., 10, North-Holland, Amsterdam, 1987, 477–513 | MR | Zbl

[15] J. Soviet Math., 22:4 (1983), 1401–1475 | DOI | Zbl

[16] F. Cossec, “Reye congruences”, Trans. Amer. Math. Soc., 280:2 (1983), 737–751 | DOI | MR | Zbl

[17] F. R. Cossec and I. V. Dolgachev, Enriques surfaces, v. I, Progr. Math., 76, Birkhäuser, Boston, MA, 1989 | MR | Zbl

[18] W. Barth and C. Peters, “Automorphisms of Enriques surfaces”, Invent. Math., 73:3 (1983), 383–411 | DOI | MR | Zbl

[19] F. Cossec and I. Dolgachev, “On automorphisms of nodal Enriques surfaces”, Bull. Amer. Math. Soc., 12:2 (1985), 247–249 | DOI | MR | Zbl

[20] F. Catanese, “On the rationality of certain moduli spaces related to curves of genus 4”, Algebraic geometry (Ann Arbor, MI 1981), Lecture Notes in Math., 1008, Springer-Verlag, Berlin, 1983, 30–50 | DOI | MR | Zbl

[21] A. Beauville, “Variétés de Prym et jacobiennes intermediaires”, Ann. Sci. École Norm. Sup. (4), 10:3 (1977), 309–391 | MR | Zbl

[22] I. Dolgachev, “Enriques surfaces: what is left?”, Problems in the theory of surfaces and their classification (Cortona 1988), Sympos. Math., 32, Academic Press, London, 1991, 81–97 | MR | Zbl