An analogue of the Novikov Conjecture in complex algebraic geometry
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Abstract:
We introduce an analogue of the Novikov Conjecture on higher signatures in the context of the algebraic geometry of (nonsingular) complex projective varieties. This conjecture asserts that certain “higher Todd genera” are birational invariants. This implies birational invariance of certain extra combinations of Chern classes (beyond just the classical Todd genus) in the case of varieties with large fundamental group (in the topological sense). We prove the conjecture under the assumption of the “strong Novikov Conjecture” for the fundamental group, which is known to be correct for many groups of geometric interest. We also show that, in a certain sense, our conjecture is best possible.References
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Additional Information
- Jonathan Rosenberg
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- MR Author ID: 298722
- ORCID: 0000-0002-1531-6572
- Email: jmr@math.umd.edu
- Received by editor(s): February 20, 2006
- Published electronically: June 13, 2007
- Additional Notes: This work was partially supported by NSF grant number DMS-0504212.
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 383-394
- MSC (2000): Primary 14E05; Secondary 32Q55, 57R77, 58J20, 58J22, 46L87
- DOI: https://doi.org/10.1090/S0002-9947-07-04320-6
- MathSciNet review: 2342008