@incollection{AST_2009__328__355_0, author = {Yoshikawa, Ken-Ichi}, title = {Calabi-Yau threefolds of {Borcea-Voisin,} analytic torsion, and {Borcherds} products}, booktitle = {From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut}, editor = {Dai Xianzhe and L\'eandre R\'emi and Xiaonan Ma and Zhang Weiping}, series = {Ast\'erisque}, pages = {355--393}, publisher = {Soci\'et\'e math\'ematique de France}, number = {328}, year = {2009}, mrnumber = {2674883}, zbl = {1200.14075}, language = {en}, url = {http://archive.numdam.org/item/AST_2009__328__355_0/} }
TY - CHAP AU - Yoshikawa, Ken-Ichi TI - Calabi-Yau threefolds of Borcea-Voisin, analytic torsion, and Borcherds products BT - From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut AU - Collectif ED - Dai Xianzhe ED - Léandre Rémi ED - Xiaonan Ma ED - Zhang Weiping T3 - Astérisque PY - 2009 SP - 355 EP - 393 IS - 328 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_2009__328__355_0/ LA - en ID - AST_2009__328__355_0 ER -
%0 Book Section %A Yoshikawa, Ken-Ichi %T Calabi-Yau threefolds of Borcea-Voisin, analytic torsion, and Borcherds products %B From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut %A Collectif %E Dai Xianzhe %E Léandre Rémi %E Xiaonan Ma %E Zhang Weiping %S Astérisque %D 2009 %P 355-393 %N 328 %I Société mathématique de France %U http://archive.numdam.org/item/AST_2009__328__355_0/ %G en %F AST_2009__328__355_0
Yoshikawa, Ken-Ichi. Calabi-Yau threefolds of Borcea-Voisin, analytic torsion, and Borcherds products, dans From probability to geometry (II) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 328 (2009), pp. 355-393. http://archive.numdam.org/item/AST_2009__328__355_0/
[1] Compact complex surfaces, Ergebnisse Math. Grenzg. (3), vol. 4, Springer, 1984. | MR | Zbl
, & -[2] Holomorphic anomalies in topological field theories", Nuclear Phys. B 405 (1993), p. 279-304. | DOI | MR | Zbl
, , & - "[3] Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes", Comm. Math. Phys. 165 (1994), p. 311-427. | DOI | MR | Zbl
, , & , "[4] Equivariant immersions and Quillen metrics", J. Differential Geom. 41 (1995), p. 53-157. | DOI | MR | Zbl
- "[5] Quillen metrics and singular fibres in arbitrary relative dimension", J. Algebraic Geom. 6 (1997), p. 19-149. | MR | Zbl
, "[6] Fibrés déterminants, métriques de Quillen et dégénérescence des courbes", Acta Math. 165 (1990), p. 1-103. | DOI | MR | Zbl
& - "[7] Analytic torsion and holomorphic determinant bundles I, II, III", Commun. Math. Phys. 115 (1988), p. 49-78, 79-126, 301-351. | DOI | MR | Zbl
, & - "[8] Complex immersions and Quillen metrics", Publ. Math. I.H.É.S. 74 (1991). | EuDML | Numdam | MR | Zbl
& - "[9] surfaces with involution and mirror pairs of Calabi-Yau manifolds", in Mirror symmetry, II, AMS/IP Stud. Adv. Math., vol. 1, Amer. Math. Soc., 1997, p. 717-743. | MR | Zbl
- "[10] Monstrous moonshine and monstrous Lie superalgebras", Invent. Math. 109 (1992), p. 405-444. | DOI | EuDML | MR | Zbl
- "[11] The moduli space of Enriques surfaces and the fake Monster Lie superalgebra", Topology 35 (1996), p. 699-710. | DOI | MR | Zbl
, "[12] Automorphic forms with singularities on Grassmannians", Invent. Math. 132 (1998), p. 491-562. | DOI | MR | Zbl
, "[13] On the Torelli problem for kählerian surfaces", Ann. Sci. École Norm. Sup. 8 (1975), p. 235-273. | DOI | EuDML | Numdam | MR | Zbl
& - "[14] Analytic torsion for Calabi-Yau threefolds", J. Differential Geom. 80 (2008), p. 175-259. | DOI | MR | Zbl
, & - "[15] Plurisubharmonische Funktionen in komplexen Räumen", Math. Z. 65 (1956), p. 175-194. | DOI | EuDML | MR | Zbl
& - "[16] surfaces, Lorentzian Kac-Moody algebras and mirror symmetry", Math. Res. Lett. 3 (1996), p. 211-229. | DOI | MR | Zbl
& - "[17] Siegel automorphic form corrections of some Lorentzian Kac-Moody Lie algebras", Amer. J. Math. 119 (1997), p. 181-224. | DOI | MR | Zbl
& , "[18] Automorphic forms and Lorentzian Kac-Moody algebras. I", Internat. J. Math. 9 (1998), p. 153-199. | DOI | MR | Zbl
& , "[19] Exact gravitational threshold correction in the Ferrara-Harvey-Strominger-Vafa model", Phys. Rev. D 57 (1998), p. 2329-2336. | DOI | MR
& - "[20] Borcherds symmetries in -theory", J. High Energy Phys. 4 (2002), No. 49, 31. | MR
, & - "[21] Relation between the denominator formulae for generalized Kac-Moody superalgebras and automorphic forms, Master's Thesis, University of Tokyo, 2000.
-[22] Geometry of bounded domains", Trans. Amer. Math. Soc. 92 (1959), p. 267-290. | DOI | MR | Zbl
- "[23] Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker Inc., 1970. | MR | Zbl
,[24] A fixed point formula of Lefschetz type in Arakelov geometry. I. Statement and proof, Invent. Math. 145 (2001), p. 333-396. | DOI | MR | Zbl
& - "[25] Submersions and equivariant Quillen metrics", Ann. Inst. Fourier (Grenoble) 50 (2000), p. 1539-1588. | DOI | EuDML | Numdam | MR | Zbl
- "[26] Formes automorphes et théorèmes de Riemann-Roch arithmétiques", preprint arXiv:0806.1765, 2008.
& - "[27] Cubic forms, second ed., North-Holland Mathematical Library, vol. 4, North-Holland Publishing Co., 1986. | MR | Zbl
-[28] Integral symmetric bilinear forms and some of their applications", Math. USSR Izv. 14 (1980), p. 103-167. | DOI | Zbl
- "[29] Factor groups of groups of automorphisms of hyperbolic forms with respect to subgroups generated by -reflections", J. Soviet Math. 22 (1983), p. 1401-1476. | DOI | Zbl
, "[30] Reflection groups in Lobachevskiï spaces and an identity for the denominator of Lorentzian Kac-Moody algebras", Izv. Ross. Akad. Nauk Ser. Mat. 60 (1996), p. 73-106. | MR | Zbl
, "[31] A Torelli theorem for algebraic surfaces of type ", Math. USSR Izv. 35 (1971), p. 530-572. | MR | Zbl
& - "[32] Determinants of Cauchy-Riemann operators over a Riemann surface", Funct. Anal Appl. 19 (1985), 31-34. | DOI | Zbl
- "[33] Analytic torsion for complex manifolds", Ann. of Math. 98 (1973), p. 154-177. | DOI | MR | Zbl
& - "[34] The fake monster superalgebra", Adv. Math. 151 (2000), p. 226-269. | DOI | MR | Zbl
- "[35] Analyticity of sets associated to Lelong numbers and the extension of closed positive currents", Invent. Math. 27 (1974), p. 53-156. | DOI | EuDML | MR | Zbl
- "[36] Miroirs et involutions sur les surfaces ", Astérisque 218 (1993), p. 273-323. | MR | Zbl
- "[37] surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space", Invent. Math. 156 (2004), p. 53-117. | DOI | MR | Zbl
- "[38] surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space II: A structure theorem", preprint http://kyokan.ms.u-tokyo.ac.jp/users/preprint/pdf/2007-12.pdf, 2007. | Zbl
, "[39] On the singularity of Quillen metrics", Math. Ann. 337 (2007), p. 61-89. | DOI | MR | Zbl
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