Transactions of the American Mathematical Society

Author(s): Jonathan Rosenberg
Journal: Trans. Amer. Math. Soc. 360 (2008), 383-394.
MSC (2000): Primary 14E05; Secondary 32Q55, 57R77, 58J20, 58J22, 46L87
Posted: June 13, 2007
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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.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14E05, 32Q55, 57R77, 58J20, 58J22, 46L87

Jonathan Rosenberg
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: jmr@math.umd.edu

DOI: 10.1090/S0002-9947-07-04320-6
PII: S 0002-9947(07)04320-6
Keywords: Birational invariant, Novikov Conjecture, Todd class, complex projective variety, characteristic number, Mishchenko-Fomenko index
Received by editor(s): February 20, 2006
Posted: June 13, 2007
Additional Notes: This work was partially supported by NSF grant number DMS-0504212.
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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