Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MMO_2017_78_1_a3, author = {Valery Gritsenko and Viacheslav V. Nikulin}, title = {Examples of lattice-polarized $K3$ surfaces with automorphic discriminant, and {Lorentzian} {Kac--Moody} algebras}, journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva}, pages = {89--100}, publisher = {mathdoc}, volume = {78}, number = {1}, year = {2017}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MMO_2017_78_1_a3/} }
TY - JOUR AU - Valery Gritsenko AU - Viacheslav V. Nikulin TI - Examples of lattice-polarized $K3$ surfaces with automorphic discriminant, and Lorentzian Kac--Moody algebras JO - Trudy Moskovskogo matematičeskogo obŝestva PY - 2017 SP - 89 EP - 100 VL - 78 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MMO_2017_78_1_a3/ LA - ru ID - MMO_2017_78_1_a3 ER -
%0 Journal Article %A Valery Gritsenko %A Viacheslav V. Nikulin %T Examples of lattice-polarized $K3$ surfaces with automorphic discriminant, and Lorentzian Kac--Moody algebras %J Trudy Moskovskogo matematičeskogo obŝestva %D 2017 %P 89-100 %V 78 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/MMO_2017_78_1_a3/ %G ru %F MMO_2017_78_1_a3
Valery Gritsenko; Viacheslav V. Nikulin. Examples of lattice-polarized $K3$ surfaces with automorphic discriminant, and Lorentzian Kac--Moody algebras. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 78 (2017) no. 1, pp. 89-100. http://geodesic.mathdoc.fr/item/MMO_2017_78_1_a3/
[1] Borcherds R. E., “Generalized Kac — Moody algebras”, J. Algebra, 115 (1988), 501–512 | DOI | MR | Zbl
[2] Borcherds R. E., “Automorphic forms on $\mathrm{O}_{s+2,2}(\mathbf R)$ and infinite products”, Invent. Math., 120:1 (1995), 161–213 | DOI | MR | Zbl
[3] Borcherds R. E., “The moduli space of Enriques surfaces and the fake Monster Lie superalgebra”, Topology, 35 (1996), 699–710 | DOI | MR | Zbl
[4] Burns D., Rapoport M., “On the Torelli problem for Kählerian $K$-3 surfaces”, Ann. Sci. École Norm. Sup. (4), 8:2 (1975), 235–273 | DOI | MR | Zbl
[5] Conway J. H., Sloane N. J. A., Sphere packings, lattices and groups, Grundlehren der Mathematischen Wissenschaften, 290, Springer-Verlag, New York, 1988 | DOI | MR | Zbl
[6] Dolgachev I. V., “Zerkalnaya simmetriya dlya polyarizovannykh $K3$-poverkhnostei”, Algebraicheskaya geometriya – 4, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 33, VINITI, M., 2001, 20–71
[7] Dolgachev I. V., Nikulin V. V., “Isklyuchitelnye osobennosti V. I. Arnolda i $K3$–poverkhnosti”, Vsesoyuznaya topologicheskaya konferentsiya v Minske, tezisy, Minskii gos. un-t, Minsk, 1977
[8] Gritsenko V., Reflective modular forms in algebraic geometry, 2010, arXiv: math/1005.3753
[9] Gritsenko V., Hulek K., “Uniruledness of orthogonal modular varieties”, J. Algebraic Geom., 23 (2014), 711–725 | DOI | MR | Zbl
[10] Gritsenko V., Hulek K., Sankaran G. K., “Abelianisation of orthogonal groups and the fundamental group of modular varieties”, J. Algebra, 322 (2009), 463–478 | DOI | MR | Zbl
[11] Gritsenko V. A., Nikulin V. V., “$K3$ surfaces, Lorentzian Kac — Moody algebras and mirror symmetry”, Math. Res. Lett., 3:2 (1996), 211–229, arXiv: alg-geom/9510008 | DOI | MR | Zbl
[12] Gritsenko V. A., Nikulin V. V., “The arithmetic mirror symmetry and Calabi — Yau manifolds”, Comm. Math. Phys., 210 (2000), 1–11, arXiv: alg-geom/9612002 | DOI | MR | Zbl
[13] Gritsenko V. A., Nikulin V. V., Lorentzian Kac — Moody algebras with Weyl groups of 2–reflections, 2016, arXiv: 1602.08359 | MR
[14] Gritsenko V. A., Nikulin V. V., Examples of lattice-polarized $K3$ surfaces with automorphic discriminant, and Lorentzian Kac — Moody algebras, 2017, arXiv: 1702.07551 | MR
[15] Kac V., Infinite dimensional Lie algebras, Cambridge Univ. Press, 1990 | MR | Zbl
[16] Kac V., “Lie superalgebras”, Adv. Math., 26 (1977), 8–96 | DOI | MR | Zbl
[17] Kulikov Vik. S., “Vyrozhdeniya $K3$-poverkhnostei i poverkhnostei Enrikvesa”, Izv. AN SSSR. Ser. matem., 41:5 (1977), 1008–1042 | MR | Zbl
[18] Looijenga E., “Compactifications defined by arrangements. II. Locally symmetric varieties of type IV”, Duke Math. J., 119:3 (2003), 527–588, arXiv: math/0201218 | DOI | MR | Zbl
[19] Ma S., On the Kodaira dimension of orthogonal modular varieties, arXiv: 1701.03225 | MR
[20] Nikulin V. V., “Konechnye gruppy avtomorfizmov kelerovykh poverkhnostei tipa $K3$”, Trudy MMO, 38, Izd-vo Moskovskogo un-ta, M., 1979, 75–137
[21] Nikulin V. V., “Tselochislennye simmetricheskie bilineinye formy i nekotorye ikh geometricheskie prilozheniya”, Izv. AN SSSR. Ser. matem, 43:1 (1979), 111–177 | MR | Zbl
[22] Nikulin V. V., “O faktorgruppakh grupp avtomorfizmov giperbolicheskikh form po podgruppam, porozhdënnym 2-otrazheniyami. Algebro-geometricheskie prilozheniya”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat., 18, VINITI, M., 1981, 3–114
[23] Nikulin V. V., “Poverkhnosti tipa $K3$ s konechnoi gruppoi avtomorfizmov i gruppoi Pikara ranga tri”, Algebraicheskaya geometriya i ee prilozheniya, Sbornik statei, Tr. MIAN SSSR, 165, 1984, 119–142 | Zbl
[24] Nikulin V. V., “Zamechanie o diskriminantakh mnogoobrazii modulei poverkhnostei $K3$ kak mnozhestv nulei avtomorfnykh form”, Algebraicheskaya geometriya – 4, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 33, VINITI, M., 2001, 242–250
[25] Pyatetskii-Shapiro I. I., Shafarevich I. R., “Teorema Torelli dlya algebraicheskikh poverkhnostei tipa $K3$”, Izv. AN SSSR. Ser. matem, 35:3 (1979), 530–572
[26] Siu Y.-T., “A simple proof of the surjectivity of the period map of $K3$ surfaces”, Manuscripta Math, 35:3 (1981), 311–321 | DOI | MR | Zbl
[27] Todorov A., “Applications of the Kähler — Einstein — Calabi — Yau metric to moduli of $K3$ surfaces”, Invent. Math., 61:3 (1981), 251–265 | DOI | MR
[28] Trans. Moscow Math. Soc., 2007, 39–66 | Zbl