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Iversen's formula for the second Chern classes of regular surfaces in any characteristic
Author(s):
I.
B.
Zhukov
Translated by:
the author
Original publication:
Algebra i Analiz,
tom 19
(2007),
nomer 5.
Journal:
St. Petersburg Math. J.
19
(2008),
775-791.
MSC (2000):
Primary 14J29
Posted:
June 25, 2008
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Additional information
Abstract:
The formula mentioned in the title is proved.
References:
-
- [Br]
- J.-L. Brylinski, Théorie du corps de classes de Kato et revêtements abéliens de surfaces, Ann. Inst. Fourier (Grenoble) 33 (1983), no. 3, 23-38. MR 0723946 (85f:11088)
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- P. Deligne, Letter to L. Illusie of 28.11.76, not published.
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- W. Fulton, Intersection theory, 2nd ed., Ergeb. Math. Grenzgeb. (3) Ser. Modern Surveys in Math., Bd. 2, Springer-Verlag, Berlin, 1998. MR 1644323 (99d:14003)
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- S. Iitaka, Algebraic geometry. An introduction to birational geometry of algebraic varieties, Grad. Texts in Math., Bd. 76, Springer-Verlag, New York-Berlin, 1982. MR 0637060 (84j:14001)
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- B. Iversen, Numerical invariants and multiple planes, Amer. J. Math. 92 (1970), 968-996. MR 0296074 (45:5135)
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- A. N. Parshin, Chern classes, adèles and
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- I. R. Shafarevich, Basic algebraic geometry. Vols. 1, 2, 2nd ed., ``Nauka'', Moscow, 1988; English transl., Springer-Verlag, Berlin, 1994. MR 0969372 (90g:14001); MR 0979764 (90g:14002); MR 1328833 (95m:14001); MR 1328834 (95m:14002)
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- H. Yamada, Rational sections and Chern classes of vector bundles, J. Math. Kyoto Univ. 6 (1967), no. 2, 295-312. MR 0209298 (35:196)
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Additional Information:
I.
B.
Zhukov
Affiliation:
Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Staryĭ Peterhof, St. Petersburg 198504, Russia
Email:
igor.zhukov@mail.ru
DOI:
10.1090/S1061-0022-08-01020-0
PII:
S 1061-0022(08)01020-0
Keywords:
Euler characteristic,
Chern class,
ferocious ramification,
wild different
Received by editor(s):
23/MAY/2007
Posted:
June 25, 2008
Dedicated:
Dedicated to the {\rm 100}th anniversary of D. K. Faddeev's birth
Copyright of article:
Copyright
2008,
American Mathematical Society
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