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Volumn 116, Issue 2, 2003, Pages 319-351

Elliptic genera of singular varieties

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EID: 0037332212     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-03-11625-7     Document Type: Article
Times cited : (66)

References (40)
  • 2
    • 0001579635 scopus 로고
    • The index of elliptic operators, III
    • MR 38:5245
    • M. F. ATIYAH and I. M. SINGER, The index of elliptic operators, III, Ann. of Math. (2) 87 (1968), 546-604. MR 38:5245
    • (1968) Ann. of Math. , vol.87 , Issue.2 , pp. 546-604
    • Atiyah, M.F.1    Singer, I.M.2
  • 3
    • 0002840891 scopus 로고    scopus 로고
    • Stringy Hodge numbers of varieties with Gorenstein canonical singularities
    • World Sci., River Edge, N.J., MR 2001a:14039
    • V. V. BATYREV, "Stringy Hodge numbers of varieties with Gorenstein canonical singularities" in Integrable Systems and Algebraic Geometry (Kobe/Kyoto, 1997), World Sci., River Edge, N.J., 1998, 1-32. MR 2001a:14039
    • (1998) Integrable Systems and Algebraic Geometry (Kobe/Kyoto, 1997) , pp. 1-32
    • Batyrev, V.V.1
  • 4
    • 0003375118 scopus 로고    scopus 로고
    • Birational Calabi-Yau n-folds have equal Betti numbers
    • New Trends in Algebraic Geometry (Warwick, England, 1996), Cambridge Univ. Press, Cambridge, MR 2000i:14059
    • _, "Birational Calabi-Yau n-folds have equal Betti numbers" in New Trends in Algebraic Geometry (Warwick, England, 1996), London Math. Soc. Lecture Note Ser. 264, Cambridge Univ. Press, Cambridge, 1999, 1-11. MR 2000i:14059
    • (1999) London Math. Soc. Lecture Note Ser. , vol.264 , pp. 1-11
  • 5
    • 0003189255 scopus 로고    scopus 로고
    • Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs
    • MR 2001j:14018
    • _, Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs, J. Eur. Math. Soc. (JEMS) 1 (1999), 5-33. MR 2001j:14018
    • (1999) J. Eur. Math. Soc. (JEMS) , vol.1 , pp. 5-33
  • 7
    • 0030268719 scopus 로고    scopus 로고
    • Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry
    • MR 97e:14023
    • V. V. BATYREV and D. I. DAIS, Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry, Topology 35 (1996), 901-929. MR 97e:14023
    • (1996) Topology , vol.35 , pp. 901-929
    • Batyrev, V.V.1    Dais, D.I.2
  • 8
    • 0031486450 scopus 로고    scopus 로고
    • Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
    • MR 98e:14010
    • E. BIERSTONE and P. MILMAN, Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant, Invent. Math. 128 (1997), 207-302. MR 98e:14010
    • (1997) Invent. Math. , vol.128 , pp. 207-302
    • Bierstone, E.1    Milman, P.2
  • 9
    • 0003340157 scopus 로고
    • Intersection cohomology (Bern, 1983)
    • Swiss Seminars, Birkhäuser, Boston, MR 88d:32024
    • A. BOREL ET AL., Intersection Cohomology (Bern, 1983), Progr. Math. 50, Swiss Seminars, Birkhäuser, Boston, 1984. MR 88d:32024
    • (1984) Progr. Math. , vol.50
    • Borel, A.1
  • 10
    • 0035530551 scopus 로고    scopus 로고
    • Vertex algebras and mirror symmetry
    • MR 2002f:17046
    • L. A. BORISOV, Vertex algebras and mirror symmetry, Comm. Math. Phys. 215 (2001), 517-557. MR 2002f:17046
    • (2001) Comm. Math. Phys. , vol.215 , pp. 517-557
    • Borisov, L.A.1
  • 12
    • 0034349013 scopus 로고    scopus 로고
    • Elliptic genera of toric varieties and applications to mirror symmetry
    • MR 2001j:58037
    • L. A. BORISOV and A. LIBGOBER, Elliptic genera of toric varieties and applications to mirror symmetry, Invent. Math. 140 (2000), 453-485. MR 2001j:58037
    • (2000) Invent. Math. , vol.140 , pp. 453-485
    • Borisov, L.A.1    Libgober, A.2
  • 14
    • 0003270876 scopus 로고
    • Elliptic functions
    • Springer, Berlin, MR 87e:11058
    • K. CHANDRASEKHARAN, Elliptic Functions, Grundlehren Math. Wiss. 281, Springer, Berlin, 1985. MR 87e:11058
    • (1985) Grundlehren Math. Wiss. , vol.281
    • Chandrasekharan, K.1
  • 15
    • 0002847615 scopus 로고
    • Higher-dimensional complex geometry
    • Soco Math. France, Montrouge, MR 90j:14046
    • H. CLEMENS, J. KOLLÁR, and S. MORI, Higher-Dimensional Complex Geometry, Astérisque 166, Soco Math. France, Montrouge, 1988. MR 90j:14046
    • (1988) Astérisque , vol.166
    • Clemens, H.1    Kollár, J.2    Mori, S.3
  • 16
    • 0001780914 scopus 로고
    • The geometry of toric varieties
    • V. I. DANILOV, The geometry of toric varieties (in Russian), Uspekhi Mat. Nauk 33, no. 2 (1978), 85-134; English translation in Russian Math. Surveys 33, no. 2 (1978), 97-154. MR 80g:14001
    • (1978) Uspekhi Mat. Nauk , vol.33 , Issue.2 , pp. 85-134
    • Danilov, V.I.1
  • 17
    • 0013503306 scopus 로고
    • English translation in Russian. MR 80g:14001
    • V. I. DANILOV, The geometry of toric varieties (in Russian), Uspekhi Mat. Nauk 33, no. 2 (1978), 85-134; English translation in Russian Math. Surveys 33, no. 2 (1978), 97-154. MR 80g:14001
    • (1978) Math. Surveys , vol.33 , Issue.2 , pp. 97-154
  • 18
    • 0033248102 scopus 로고    scopus 로고
    • Germs of arcs on singular algebraic varieties and motivic integration
    • MR 99k:14002
    • J. DENEF and F. LOESER, Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math. 135 (1999), 201-232. MR 99k:14002
    • (1999) Invent. Math. , vol.135 , pp. 201-232
    • Denef, J.1    Loeser, F.2
  • 20
    • 0001399319 scopus 로고    scopus 로고
    • Elliptic genera of symmetric products and second quantized strings
    • MR 98g:81191
    • R. DIJKGRAAF, G. MOORE, E. VERLINDE, and H. VERLINDE, Elliptic genera of symmetric products and second quantized strings, Comm. Math. Phys. 185 (1997), 197-209. MR 98g:81191
    • (1997) Comm. Math. Phys. , vol.185 , pp. 197-209
    • Dijkgraaf, R.1    Moore, G.2    Verlinde, E.3    Verlinde, H.4
  • 21
    • 0002758570 scopus 로고
    • The theory of Jacobi forms
    • Birkhäuser, Boston, MR 86j:11043
    • M. EICHLER and D. ZAGIER, The Theory of Jacobi Forms, Progr. Math. 55, Birkhäuser, Boston, 1985. MR 86j:11043
    • (1985) Progr. Math. , vol.55
    • Eichler, M.1    Zagier, D.2
  • 22
    • 0347036558 scopus 로고    scopus 로고
    • On the cobordism class of the Hilbert scheme of a surface
    • MR 2001k:14005
    • G. ELLINGSRUD, L. GÖTTSCHE, and M. LEHN, On the cobordism class of the Hilbert scheme of a surface, J. Algebraic Geom. 10 (2001), 81-100. MR 2001k:14005
    • (2001) J. Algebraic Geom. , vol.10 , pp. 81-100
    • Ellingsrud, G.1    Göttsche, L.2    Lehn, M.3
  • 23
    • 0000975014 scopus 로고
    • Algebraic families on an algebraic surface
    • MR 38:5778
    • J. FOGARTY, Algebraic families on an algebraic surface, Amer. J. Math. 90 (1968), 511-521. MR 38:5778
    • (1968) Amer. J. Math. , vol.90 , pp. 511-521
    • Fogarty, J.1
  • 24
    • 0004233493 scopus 로고    scopus 로고
    • Intersection theory, 2d ed.
    • Springer, Berlin, MR 99d:14003
    • W. FULTON, Intersection Theory, 2d ed., Ergeb. Math. Grenzgeb. (3) 2, Springer, Berlin, 1998. MR 99d:14003
    • (1998) Ergeb. Math. Grenzgeb. , vol.2 , Issue.3
    • Fulton, W.1
  • 25
    • 0000372598 scopus 로고
    • Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces
    • MR 94i:14026
    • L. GÖTTSCHE and W. SOERGEL, Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces, Math. Ann. 296 (1993), 235-245. MR 94i:14026
    • (1993) Math. Ann. , vol.296 , pp. 235-245
    • Göttsche, L.1    Soergel, W.2
  • 26
    • 0002667315 scopus 로고    scopus 로고
    • Elliptic genus of Calabi-Yau manifolds and Jacobi and Siegel modular forms
    • V. GRITSENKO, Elliptic genus of Calabi-Yau manifolds and Jacobi and Siegel modular forms (in Russian), Algebra i Analiz 11, no. 5 (1999), 100-125; English translation in St. Petersburg Math. J. 11, no. 5 (2000), 781-804. MR 2001i:11051
    • (1999) Algebra i Analiz , vol.11 , Issue.5 , pp. 100-125
    • Gritsenko, V.1
  • 27
    • 0000542292 scopus 로고    scopus 로고
    • English translation in MR 2001i:11051
    • V. GRITSENKO, Elliptic genus of Calabi-Yau manifolds and Jacobi and Siegel modular forms (in Russian), Algebra i Analiz 11, no. 5 (1999), 100-125; English translation in St. Petersburg Math. J. 11, no. 5 (2000), 781-804. MR 2001i:11051
    • (2000) St. Petersburg Math. J. , vol.11 , Issue.5 , pp. 781-804
  • 28
    • 84972570012 scopus 로고
    • Sur quelques points d'algèbre homologique
    • MR 21:1328
    • A. GROTHENDIECK, Sur quelques points d'algèbre homologique, Tôhoku Math. J. (2) 9 (1957), 119-221. MR 21:1328
    • (1957) Tôhoku Math. J. , vol.9 , Issue.2 , pp. 119-221
    • Grothendieck, A.1
  • 29
    • 0003308596 scopus 로고
    • Topological methods in algebraic geometry
    • Springer, Berlin, MR 96c:57002
    • F. HIRZEBRUCH, Topological Methods in Algebraic Geometry, Classics Math., Springer, Berlin, 1995. MR 96c:57002
    • (1995) Classics Math.
    • Hirzebruch, F.1
  • 30
    • 0001199084 scopus 로고
    • On the Euler number of an orbifold
    • MR 91g:57038
    • F. HIRZEBRUCH and T. HÖFER, On the Euler number of an orbifold, Math. Ann. 286 (1990), 255-260. MR 91g:57038
    • (1990) Math. Ann. , vol.286 , pp. 255-260
    • Hirzebruch, F.1    Höfer, T.2
  • 31
    • 0003304316 scopus 로고
    • Representations of the permutation groups, I
    • Springer, Berlin. MR 48:4098
    • A. KERBER, Representations of the Permutation Groups, I, Lecture Notes in Math. 240, Springer, Berlin, 1971. MR 48:4098
    • (1971) Lecture Notes in Math. , vol.240
    • Kerber, A.1
  • 32
    • 0001759870 scopus 로고
    • Generators of the Zip bordism ring: Serendipity
    • MR 53:11633
    • C. KOSNIOWSKI, Generators of the Zip bordism ring: Serendipity, Math. Z. 149 (1976), 121-130. MR 53:11633
    • (1976) Math. Z. , vol.149 , pp. 121-130
    • Kosniowski, C.1
  • 33
    • 84971187053 scopus 로고
    • The Poincaré polynomial of a symmetric product
    • MR 26:764
    • I.G. MACDONALD, The Poincaré polynomial of a symmetric product, Proc. Cambridge Philos. Soc. 58 (1962), 563-568. MR 26:764
    • (1962) Proc. Cambridge Philos. Soc. , vol.58 , pp. 563-568
    • Macdonald, I.G.1
  • 35
    • 0001280810 scopus 로고
    • Graphs, singularities, and finite groups
    • The Santa Cruz Conference on Finite Groups (Santa Cruz, Calif., 1979), Amer. Math. Soc., Providence, MR 82e:20014
    • J. MCKAY, "Graphs, singularities, and finite groups" in The Santa Cruz Conference on Finite Groups (Santa Cruz, Calif., 1979), Proc. Sympos. Pure Math. 37, Amer. Math. Soc., Providence, 1980, 183-186. MR 82e:20014
    • (1980) Proc. Sympos. Pure Math. , vol.37 , pp. 183-186
    • McKay, J.1
  • 36
    • 0000266953 scopus 로고
    • Witt spaces: A geometric cycle theory for K O-homology at odd primes
    • MR 85f:57011
    • P. H. SIEGEL, Witt spaces: a geometric cycle theory for K O-homology at odd primes, Amer. J. Math. 105 (1983), 1067-1105. MR 85f:57011
    • (1983) Amer. J. Math. , vol.105 , pp. 1067-1105
    • Siegel, P.H.1
  • 37
    • 0034415144 scopus 로고    scopus 로고
    • Chern numbers of singular varieties and elliptic homology
    • MR 2001g:58037
    • B. TOTARO, Chern numbers of singular varieties and elliptic homology, Ann. of Math. (2) 151 (2000), 757-791. MR 2001g:58037
    • (2000) Ann. of Math. , vol.151 , Issue.2 , pp. 757-791
    • Totaro, B.1
  • 38
    • 51249192670 scopus 로고
    • Cobordism of pairs
    • MR 23:A2221
    • C.T.C. WALL, Cobordism of pairs, Comm. Math. Helv. 35 (1961), 135-145. MR 23:A2221
    • (1961) Comm. Math. Helv. , vol.35 , pp. 135-145
    • Wall, C.T.C.1
  • 39
    • 0013539579 scopus 로고    scopus 로고
    • Orbifold Hodge numbers of the wreath product orbifolds
    • MR 2002g:32034
    • W. WANG and J. ZHOU, Orbifold Hodge numbers of the wreath product orbifolds, J. Geom. Phys. 38 (2001), 152-169. MR 2002g:32034
    • (2001) J. Geom. Phys. , vol.38 , pp. 152-169
    • Wang, W.1    Zhou, J.2
  • 40
    • 21144466484 scopus 로고
    • Topological orbifold models and quantum cohomology rings
    • MR 94i:32045
    • E. ZASLOW, Topological orbifold models and quantum cohomology rings, Comm. Math. Phys. 156 (1993), 301-331. MR 94i:32045
    • (1993) Comm. Math. Phys. , vol.156 , pp. 301-331
    • Zaslow, E.1


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