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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Some properties of the signature of complete intersections

Author: A. Libgober
Journal: Proc. Amer. Math. Soc. 79 (1980), 373-375
MSC: Primary 14B05; Secondary 14M10, 57R19
MathSciNet review: 567975
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Abstract: We prove that: (1) The signature of complete intersections is a monotone function of degrees of defining equations.

(2) The signature of n-dimensional complete intersection (except for $ {\mathbf{C}}{{\mathbf{P}}^n}$) is positive for $ n \equiv 0 \pmod 4$ and is negative for $ n \equiv 2 \pmod 4$.

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

  • [1] F. Hirzebruch, Topological methods in algebraic geometry, Third enlarged edition. New appendix and translation from the second German edition by R. L. E. Schwarzenberger, with an additional section by A. Borel. Die Grundlehren der Mathematischen Wissenschaften, Band 131, Springer-Verlag New York, Inc., New York, 1966. MR 0202713 (34 #2573)
  • [2] John W. Wood, A connected sum decomposition for complete intersections, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 191–193. MR 520536 (80g:57050)

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PII: S 0002-9939(1980)0567975-9
Article copyright: © Copyright 1980 American Mathematical Society