Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



$K$-equivalence in birational geometry and characterizations of complex elliptic genera

Author: Chin-Lung Wang
Journal: J. Algebraic Geom. 12 (2003), 285-306
Published electronically: September 26, 2002
MathSciNet review: 1949645
Full-text PDF

Abstract | References | Additional Information

Abstract: We show that for smooth complex projective varieties the most general combinations of Chern numbers that are invariant under the $K$-equivalence relation consist of the complex elliptic genera.

References [Enhancements On Off] (What's this?)

  • 1. D. Abramovich, K.Karu, K. Matsuki and J. Wlodarsczyk; Torifications and factorizations of birational maps, preprint 1999, mathAG/9904135.
  • 2. L. Ahlfors; Complex Analysis, McGraw-Hill 1979.
  • 3. V. Batyrev; Stringy Hodge numbers of varieties with Gorenstein canonical singularities. math.AG/9711008.
  • 4. L. Borisov and A. Libgober; Elliptic genera of singular varieties, preprint 2000, math.AG/0007108.
  • 5. J. Denef and F. Loeser; Germs of arcs on singular algebraic varieties and motivic integration, Inv. Math. 135 (1999), 201-232.
  • 6. W. Fulton; Intersection Theory, Erge. Math. ihr. Gren.;3. Folge, Bd 2, Springer-Verlag 1984.
  • 7. F. Hirzebruch; Topological Methods in Algebraic Geometry, Grund. der Math. Wissen. 131, Springer 1966.
  • 8. F. Hirzebruch, T. Berger and R. Jung; Manifolds and Modular Forms, Max-Plank-Institut für Math. 1992.
  • 9. D. Huybrechts; Birational symplectic manifolds and their deformations, J. Diff. Geom. 45 (1997).
  • 10. D. Huybrechts; Compact hyperkähler manifolds: basic results, Invent. Math. 135 (1999), 63-113. Erratum math.AG/0106014.
  • 11. J. Kollár; Flops, Nagoya Math. J. 113 (1989), 15-36.
  • 12. J. Kollár and S. Mori; Classification of three dimensional flips, J. AMS 5 No.3 (1992), 533-703.
  • 13. I. Krichever; Generalized elliptic genera and Baker-Akhiezer functions, Math. Notes 47 (1990), 132-142.
  • 14. J. Milnor; On the cobordism ring $\Omega^\ast$ and a complex analogue, Amer. J. Math. 82 (1960), 505-521.
  • 15. Y. Ruan; Surgery, quantum cohomology and birational geometry, preprint 1998, math.AG/9810039.
  • 16. B. Totaro; Chern numbers for singular varieties and elliptic homology, to appear in Annals of Math. 2000.
  • 17. C.-L. Wang; On the topology of birational minimal models, J. Diff. Geom. 50 (1998), 129-146.
  • 18. J. Wlodarsczyk; Combinatorial structures on toroidal varieties and a proof of the weak factorization theorems, preprint 1999, math.AG/9904076.

Additional Information

Chin-Lung Wang
Affiliation: Department of Mathematics, National Tsing-Hua University, Hsinchu, Taiwan

Received by editor(s): October 30, 2000
Published electronically: September 26, 2002
Additional Notes: Supported in part by NSC project 89-2115-M-007-045

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
AMS Website