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Elliptic genera of level N for complete intersections
Received date: 10 Dec 2020
Accepted date: 25 Feb 2021
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We focus on the elliptic genera of level N at the cusps of a congruence subgroup for any complete intersection. Writing the first Chern class of a complete intersection as a product of an integral coefficient c1 and a generator of the 2nd integral cohomology group, we mainly discuss the values of the elliptic genera of level N for the complete intersection in the cases of c1>, =, or<0, In particular, the values about the Todd genus, , and Ak-genus can be derived from the elliptic genera of level N.
Jianbo WANG , Yuyu WANG , Zhiwang YU . Elliptic genera of level N for complete intersections[J]. Frontiers of Mathematics in China, 2021 , 16(4) : 1043 -1062 . DOI: 10.1007/s11464-021-0917-6
1 |
Atiyah M, Hirzebruch F. Spin-manifolds and group actions. In: Haeiger A, Narasimhan R, eds. Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham). Berlin: Springer, 1970, 18–28
|
2 |
Benoist O. Séparation et propriétéde Deligne-Mumford des champs de modules d'intersections complétes lisse. J Lond Math Soc, 2013, 87(2): 138–156
|
3 |
Brooks R. The A^−genus of complex hypersurfaces and complete intersections. Proc Amer Math Soc, 1983, 87(3): 528–532
|
4 |
Chen B Y. Euler characteristics and codimension of complete intersections. Proc Amer Math Soc, 1978, 71(1): 13–14
|
5 |
Dessai A, Wiemeler M. Complete intersections with S1-action. Transform Groups, 2017, 22(2): 295–320
|
6 |
Ewing J, Moolgavkar S. Euler characteristics of complete intersections. Proc Amer Math Soc, 1976, 56: 390–391
|
7 |
Fel'dman K È. Hirzebruch genus of a manifold supporting a Hamiltonian circle action. Russian Math Surveys, 2001, 56: 978–979
|
8 |
Herrera R. Elliptic genera of level N on complex π2 finite manifolds. C R Math Acad Sci Paris, Ser I, 2007, 344(5): 317–320
|
9 |
Hirzebruch F. Elliptic genera of level N for complex manifolds. In: Bleuler K, Werner M, eds. Differential Geometrical Methods in Theoretical Physics. Proceedings of the NATO Advanced Research Workshop and the Sixteenth International Conference held in Como, August 24-29, 1987. NATO Adv Sci Inst Ser C Math Phys Sci, 250. Dordrecht: Kluwer Academic Publishers Group, 1988, 37–63
|
10 |
Hirzebruch F. Topological Methods in Algebraic Geometry. Classics in Math. Berlin: Springer-Verlag, 1995
|
11 |
Hirzebruch F, Berger T, Jung R. Manifolds and Modular Forms. Aspects of Math, Vol E20. Braunschweig: Friedr Vieweg and Sohn, 1992
|
12 |
Kobayashi S. Transformation Groups in Differential Geometry. Classics in Math. Berlin: Springer-Verlag, 1995
|
13 |
Krichever I M. Obstructions to the existence of S1-actions. Bordism of ramified coverings. Izv Akad Nauk SSSR Ser Mat, 1976, 40: 828-844 (in Russian); Math USSR-Izv, 1976, 10: 783–797
|
14 |
Krichever I M. Generalized elliptic genera and Baker-Akhiezer functions. Mat Zametki, 1990, 47: 34-45 (in Russian); Math Notes, 1990, 47: 132–142
|
15 |
Libgober A S. Some properties of the signature of complete intersections. Proc Amer Math Soc, 1980, 79(3): 373–375
|
16 |
Libgober A S, Wood J W. Differentiable structures on complete intersections, I. Topology, 1982, 21(4): 469–482
|
17 |
Wang J B, Yu Z W,Wang Y Y. The Hirzebruch genera of complete intersections, arXiv: 2003.02049
|
18 |
Witten E. The index of the Dirac operator in loop space. In: Landweber P S, ed. Elliptic Curves and Modular Forms in Algebraic Topology. Lecture Notes in Math, Vol 1326. Berlin: Springer, 1988, 161–181
|
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