Géométrie des espaces de modules de courbes et de surfaces $K3$ [d'après Gritsenko-Hulek-Sankaran, Farkas-Popa, Mukai, Verra, ...]

Voisin, Claire

Séminaire Bourbaki - Volume 2006/2007 - Exposés 967-981, Astérisque, no. 317 (2008), Exposé no. 981, 24 p.

[1] Geometry of $K3$ surfaces : moduli and periods (Palaiseau, 1981/1982) - 1985, Astérisque 126.

[2] E. Arbarello, M. Cornalba, P. A. Griffiths & J. Harris - Geometry of algebraic curves. Vol. I, Grundlehren der Mathematischen Wissenschaften, vol. 267, Springer, 1985. | DOI | MR | Zbl

[3] A. Ash, D. Mumford, M. Rapoport & Y.-S. Tai - Smooth compactification of locally symmetric varieties, Math. Sci. Press, 1975, Lie Groups : History, Frontiers and Applications, Vol. IV. | MR | Zbl

[4] M. F. Atiyah - On analytic surfaces with double points, Proc. Roy. Soc. London. Ser. A 247 (1958), p. 237-244. | DOI | MR | Zbl

[5] W. L. Baily, Jr. & A. Borel - Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math. (2) 84 (1966), p. 442-528. | DOI | MR | Zbl

[6] W. Barth, C. Peters & A. Van De Ven - Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 4, Springer, 1984. | Zbl

[7] A. Beauville - Surfaces $K3$, Séminaire Bourbaki, vol. 1982/83, exp. n° 609, Astérisque 105-106 (1983), p. 217-229. | EuDML | Numdam | MR | Zbl

[8] A. Beauville & J.-Y. Mérindol - Sections hyperplanes des surfaces $K3$, Duke Math. J. 55 (1987), p. 873-878. | DOI | MR | Zbl

[9] R. E. Borcherds - Automorphic forms on $O_{𝑠+2,2}\left(𝐑\right)$ and infinite products, Invent. Math. 120 (1995), p. 161-213. | DOI | EuDML | MR | Zbl

[10] R. E. Borcherds, L. Katzarkov, T. Pantev & N. I. Shepherd-Barron - Families of $K3$ surfaces, J. Algebraic Geom. 7 (1998), p. 183-193. | MR | Zbl

[11] S. Boucksom, J.-P. Demailly, M. Paun & T. Peternell - The pseudoeffective cone of a compact Kähler manifold and varieties of negative Kodaira dimension, prépublication, 2004. | Zbl

[12] M. C. Chang & Z. Ran - Unirationality of the moduli spaces of curves of genus $11,13$ (and $12$), Invent. Math. 76 (1984), p. 41-54. | DOI | EuDML | MR | Zbl

[13] C. Ciliberto, J. Harris & R. Miranda - On the surjectivity of the Wahl map, Duke Math. J. 57 (1988), p. 829-858. | DOI | MR | Zbl

[14] M. Cornalba & J. Harris - Divisor classes associated to families of stable varieties, with applications to the moduli space of curves, Ann. Sci. Ecole Norm. Sup. 4 21 (1988), p. 455-475. | DOI | EuDML | Numdam | MR | Zbl

[15] F. Cukierman & D. Ulmer - Curves of genus ten on $K3$ surfaces, Compositio Math. 89 (1993), p. 81-90. | EuDML | Numdam | MR | Zbl

[16] O. Debarre - Variétés rationnellement connexes (d'après T. Graber, J. Harris, J. Starr et A. J. de Jong), Séminaire Bourbaki, vol. 2001/2002, exp. n° 905, Astérisque 290 (2003), p. 243-266. | EuDML | Numdam | MR | Zbl

[17] P. Deligne & D. Mumford - The irreducibility of the space of curves of given genus, Publ. Math. I.H.É.S. 36 (1969), p. 75-109. | DOI | EuDML | Numdam | MR | Zbl

[18] D. Eisenbud & J. Harris - The Kodaira dimension of the moduli space of curves of genus $\ge 23$, Invent. Math. 90 (1987), p. 359-387. | DOI | EuDML | MR | Zbl

[19] G. Farkas - The geometry of the moduli space of curves of genus $23$, Math. Ann. 318 (2000), p. 43-65. | DOI | MR | Zbl

[20] G. Farkas & M. Popa - Effective divisors on ${\overline{ℳ}}_g$, curves on $K3$ surfaces, and the slope conjecture, J. Algebraic Geom. 14 (2005), p. 241-267. | DOI | MR | Zbl

[21] M. Green & R. Lazarsfeld - Special divisors on curves on a $K3$ surface, Invent. Math. 89 (1987), p. 357-370. | DOI | EuDML | MR | Zbl

[22] V. A. Gritsenko, K. Hulek & G. K. Sankaran - The Kodaira dimension of the moduli of $K3$ surfaces, Invent. Math. 169 (2007), p. 519-567. | DOI | MR | Zbl

[23] J. Harer - The second homology group of the mapping class group of an orientable surface, Invent. Math. 72 (1983), p. 221-239. | DOI | EuDML | MR | Zbl

[24] J. Harris - On the Kodaira dimension of the moduli space of curves. II. The even-genus case, Invent. Math. 75 (1984), p. 437-466. | DOI | EuDML | MR | Zbl

[25] J. Harris & D. Mumford - On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982), p. 23-88, With an appendix by William Fulton. | DOI | MR | Zbl

[26] B. Hassett & D. Hyeon - Log canonical models for the moduli space of curves : First divisorial contraction, prépublication arXivimath/0607477, à paraître dans Trans. of the AMS. | Zbl

[27] A. Hirschowitz & S. Ramanan - New evidence for Green's conjecture on syzygies of canonical curves, Ann. Sci. Ecole Norm. Sup. (4) 31 (1998), p. 145-152. | DOI | EuDML | Numdam | MR | Zbl

[28] S. Kondō - On the Kodaira dimension of the moduli space of $K3$ surfaces. II, Compositio Math. 116 (1999), p. 111-117. | DOI | MR | Zbl

[29] R. Lazarsfeld - Brill-Noether-Petri without degenerations, J. Differential Geom. 23 (1986), p. 299-307. | DOI | MR | Zbl

[30] S. Mukai - Symplectic structure of the moduli space of sheaves on an abelian or $K3$ surface, Invent. Math. 77 (1984), p. 101-116. | DOI | EuDML | MR | Zbl

[31] S. Mukai, Curves, $K3$ surfaces and Fano $3$-folds of genus $\le 10$, in Algebraic geometry and commutative algebra, Vol. I, Kinokuniya, 1988, p. 357-377. | MR | Zbl

[32] S. Mukai, Curves and $K3$ surfaces of genus eleven, in Moduli of vector bundles (Sanda, 1994; Kyoto, 1994), Lecture Notes in Pure and Appl. Math., vol. 179, Dekker, 1996, p. 189-197. | MR | Zbl

[33] S. Mukai, Polarized $K3$ surfaces of genus thirteen, in Moduli spaces and arithmetic geometry, Adv. Stud. Pure Math., vol. 45, Math. Soc. Japan, 2006, p. 315-326. | MR | Zbl

[34] D. Mumford - Towards an enumerative geometry of the moduli space of curves, in Arithmetic and geometry, Vol. II, Progr. Math., vol. 36, Birkhäuser, 1983, p. 271-328. | DOI | MR | Zbl

[35] Y. Namikawa - Toroidal compactification of Siegel spaces, Lecture Notes in Mathematics, vol. 812, Springer, 1980. | MR | Zbl

[36] V. Nikulin - Integral symmetric bilinear forms and some of their applications, Izv. Akad. Nauk SSSR Ser. Mat. 14 (1980), p. 103-167. | MR | Zbl

[37] V. Nikulin, A remark on discriminants for moduli of $K3$ surfaces as sets of zeros of automorphic forms, J. Math. Sci. 81 (1996), p. 2738-2743, | DOI | MR | Zbl

V. Nikulin, A remark on discriminants for moduli of $K3$ surfaces as sets of zeros of automorphic forms, Algebraic geometry, 4. | Zbl

[38] I. I. Pjateckiĭ-Sapiro & I. R. Safarevič - Torelli's theorem for algebraic surfaces of type $K3$, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), p. 530-572. | MR

[39] M. Reid - Young person's guide to canonical singularities, in Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Sympos. Pure Math., vol. 46, Amer. Math. Soc., 1987, p. 345-414. | DOI | MR | Zbl

[40] E. Sernesi - Unirationality of the variety of moduli of curves of genus twelve, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 8 (1981), p. 405-439. | EuDML | Numdam | MR | Zbl

[41] Y.-S. Tai - On the Kodaira dimension of the moduli space of abelian varieties, Invent. Math. 68 (1982), p. 425-439. | DOI | EuDML | MR | Zbl

[42] A. Verra - The unirationality of the moduli spaces of curves of genus $14$ or lower, Compos. Math. 141 (2005), p. 1425-1444. | DOI | MR | Zbl

[43] E. Viehweg - Quasi-projective moduli for polarized manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 30, Springer, 1995. | MR | Zbl

[44] C. Voisin - Sur l'application de Wahl des courbes satisfaisant la condition de Brill-Noether-Petri, Acta Math. 168 (1992), p. 249-272. | DOI | MR | Zbl

[45] C. Voisin, Green's generic syzygy conjecture for curves of even genus lying on a $K3$ surface, J. Eur. Math. Soc. (JEMS) 4 (2002), p. 363-404. | DOI | EuDML | MR | Zbl

[46] C. Voisin, Green's canonical syzygy conjecture for generic curves of odd genus, Compos. Math. 141 (2005), p. 1163-1190. | DOI | MR | Zbl

[47] J. M. Wahl - The Jacobian algebra of a graded Gorenstein singularity, Duke Math. J. 55 (1987), p. 843-871. | DOI | MR | Zbl