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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Genera of algebraic varieties and counting of lattice points
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by Sylvain E. Cappell and Julius L. Shaneson PDF
Bull. Amer. Math. Soc. 30 (1994), 62-69 Request permission

Abstract:

This paper announces results on the behavior of some important algebraic and topological invariants — Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. — and their associated characteristic classes, under morphisms of projective algebraic varieties. The formulas obtained relate global invariants to singularities of general complex algebraic (or analytic) maps. These results, new even for complex manifolds, are applied to obtain a version of Grothendieck-Riemann-Roch, a calculation of Todd classes of toric varieties, and an explicit formula for the number of integral points in a polytope in Euclidean space with integral vertices.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 30 (1994), 62-69
  • MSC (2000): Primary 14F45; Secondary 11P21, 14M25, 32S60
  • DOI: https://doi.org/10.1090/S0273-0979-1994-00436-7
  • MathSciNet review: 1217352