Iversen’s formula for the second Chern classes of regular surfaces in any characteristic
HTML articles powered by AMS MathViewer
- by
I. B. Zhukov
Translated by: the author - St. Petersburg Math. J. 19 (2008), 775-791
- DOI: https://doi.org/10.1090/S1061-0022-08-01020-0
- Published electronically: June 25, 2008
- PDF | Request permission
Abstract:
The formula mentioned in the title is proved.References
- Jean-Luc Brylinski, Théorie du corps de classes de Kato et revêtements abéliens de surfaces, Ann. Inst. Fourier (Grenoble) 33 (1983), no. 3, 23–38 (French, with English summary). MR 723946
- P. Deligne, Letter to L. Illusie of 28.11.76 , not published.
- William Fulton, Intersection theory, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 2, Springer-Verlag, Berlin, 1998. MR 1644323, DOI 10.1007/978-1-4612-1700-8
- G.-M. Greuel and H. Kröning, Simple singularities in positive characteristic, Math. Z. 203 (1990), no. 2, 339–354. MR 1033443, DOI 10.1007/BF02570742
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
- G. Laumon, Semi-continuité du conducteur de Swan (d’après P. Deligne), The Euler-Poincaré characteristic (French), Astérisque, vol. 82, Soc. Math. France, Paris, 1981, pp. 173–219 (French). MR 629128
- Herbert Kurke, Vorlesungen über algebraische Flächen, Teubner-Texte zur Mathematik [Teubner Texts in Mathematics], vol. 43, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1982 (German). With English, French and Russian summaries. MR 680403
- Shigeru Iitaka, Algebraic geometry, North-Holland Mathematical Library, vol. 24, Springer-Verlag, New York-Berlin, 1982. An introduction to birational geometry of algebraic varieties. MR 637060
- Birger Iversen, Numerical invariants and multiple planes, Amer. J. Math. 92 (1970), 968–996. MR 296074, DOI 10.2307/2373405
- A. N. Parshin, Chern classes, adèles and $L$-functions, J. Reine Angew. Math. 341 (1983), 174–192. MR 697316, DOI 10.1515/crll.1983.341.174
- Pierre Samuel, Singularités des variétés algébriques, Bull. Soc. Math. France 79 (1951), 121–129 (French). MR 52832
- Jean-Pierre Serre, Corps locaux, Publications de l’Institut de Mathématique de l’Université de Nancago, VIII, Hermann, Paris, 1962 (French). MR 0150130
- I. R. Shafarevich, Osnovy algebraicheskoĭ geometrii. Tom 1, 2nd ed., “Nauka”, Moscow, 1988 (Russian). Algebraicheskie mnogoobraziya v proektivnom prostranstve. [Algebraic varieties in projective space]. MR 969372
- Hiroshi Yamada, Rational sections and Chern classes of vector bundles, J. Math. Kyoto Univ. 6 (1967), 295–312. MR 209298, DOI 10.1215/kjm/1250524378
Bibliographic 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
- Received by editor(s): May 23, 2007
- Published electronically: June 25, 2008
- Additional Notes: A considerable part of this research was done during the author’s stay at Humboldt Univerität zu Berlin under the support of the Alexander von Humboldt Foundation and at the Max-Planck-Institut für Mathematik in Bonn. The work was completed under the support of the Rückkehrstipendium of the Humboldt Foundation and INTAS grant. I am very much grateful to all these organizations. Also, I would like to thank A. N. Parshin and H. Kurke for numerous inspiring discussions.
- © Copyright 2008 American Mathematical Society
- Journal: St. Petersburg Math. J. 19 (2008), 775-791
- MSC (2000): Primary 14J29
- DOI: https://doi.org/10.1090/S1061-0022-08-01020-0
- MathSciNet review: 2381944
Dedicated: Dedicated to the 100th anniversary of D. K. Faddeev’s birth