RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

 Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 2, Pages 143–162 (Mi izv16)

On the monodromy and mixed Hodge structure on cohomology of the infinite cyclic covering of the complement to a plane algebraic curve

Vik. S. Kulikova, V. S. Kulikovb

a Moscow State Academy of Printing Arts
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The semisimplicity is proved of the Alexander automorphism (the monodromy operator) on the cohomology $H^1(X_\infty)_{\ne 1}$ of the infinite cyclic covering of the complement to a plane non-reduced algebraic curve, and, in particular, the semisimplicity of $H^1(X_\infty)$ in the case of an irreducible curve. A natural mixed Hodge structure on $H^1(X_\infty)$ is introduced and the irregularity of cyclic coverings of $P^2$ is calculated in terms of the number of roots of the Alexander polynomial of the branch curve.

Full text: PDF file (2000 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 1995, 59:2, 367–386

Bibliographic databases:

Document Type: Article
MSC: 14H30

Citation: Vik. S. Kulikov, V. S. Kulikov, “On the monodromy and mixed Hodge structure on cohomology of the infinite cyclic covering of the complement to a plane algebraic curve”, Izv. RAN. Ser. Mat., 59:2 (1995), 143–162; Izv. Math., 59:2 (1995), 367–386

Citation in format AMSBIB
\Bibitem{KulKul95} \by Vik.~S.~Kulikov, V.~S.~Kulikov \paper On the monodromy and mixed Hodge structure on cohomology of the infinite cyclic covering of the complement to a~plane algebraic curve \jour Izv. RAN. Ser. Mat. \yr 1995 \vol 59 \issue 2 \pages 143--162 \mathnet{http://mi.mathnet.ru/izv16} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1337163} \zmath{https://zbmath.org/?q=an:0909.14004} \transl \jour Izv. Math. \yr 1995 \vol 59 \issue 2 \pages 367--386 \crossref{https://doi.org/10.1070/IM1995v059n02ABEH000016} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RZ88800007} 

• http://mi.mathnet.ru/eng/izv16
• http://mi.mathnet.ru/eng/izv/v59/i2/p143

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Vik. S. Kulikov, “On plane algebraic curves of positive Albanese dimension”, Izv. Math., 59:6 (1995), 1173–1192
2. G.-M. Greuel, Vik. S. Kulikov, “On symplectic coverings of the projective plane”, Izv. Math., 69:4 (2005), 667–701
3. Dimca A., Libgober A., “Regular Functions Transversal at Infinity”, Tohoku Math. J., 58:4 (2006), 549–564
•  Number of views: This page: 174 Full text: 57 References: 16 First page: 1