Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2021, Volume 85, Issue 3, Pages 73–88 (Mi izv9081)  

Plane algebraic curves in fancy balls

N. G. Kruzhilin, S. Yu. Orevkov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Boileau and Rudolph [1] called an oriented link $L$ in the 3-sphere a \textit{$\mathbb{C}$-boundary} if it can be realized as the intersection of an algebraic curve $A$ in $\mathbb{C}^2$ and the boundary of a smooth embedded closed 4-ball $B$. They showed that some links are not $\mathbb{C}$-boundaries. We say that $L$ is a \textit{strong $\mathbb{C}$-boundary} if $A\setminus B$ is connected. In particular, all quasipositive links are strong $\mathbb{C}$-boundaries.
In this paper we give examples of non-quasipositive strong $\mathbb{C}$-boundaries and non-strong $\mathbb{C}$-boundaries. We give a complete classification of (strong) $\mathbb{C}$-boundaries with at most five crossings.

Keywords: quasipositive link, $\mathbb C$-boundary, Thom conjecture.

Funding Agency Grant Number
Russian Science Foundation 19-11-00316
This work was supported by the Russian Science Foundation (project no. 19-11-00316).


DOI: https://doi.org/10.4213/im9081

Full text: PDF file (623 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2021, 85:3, 407–420

Bibliographic databases:

UDC: 515.162.8
MSC: 32S55, 57M50, 57R15, 57R95, 14H99
Received: 29.06.2020

Citation: N. G. Kruzhilin, S. Yu. Orevkov, “Plane algebraic curves in fancy balls”, Izv. RAN. Ser. Mat., 85:3 (2021), 73–88; Izv. Math., 85:3 (2021), 407–420

Citation in format AMSBIB
\Bibitem{KruOre21}
\by N.~G.~Kruzhilin, S.~Yu.~Orevkov
\paper Plane algebraic curves in fancy balls
\jour Izv. RAN. Ser. Mat.
\yr 2021
\vol 85
\issue 3
\pages 73--88
\mathnet{http://mi.mathnet.ru/izv9081}
\crossref{https://doi.org/10.4213/im9081}
\elib{https://elibrary.ru/item.asp?id=46911425}
\transl
\jour Izv. Math.
\yr 2021
\vol 85
\issue 3
\pages 407--420
\crossref{https://doi.org/10.1070/IM9081}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000671434400001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85110751282}


Linking options:
  • http://mi.mathnet.ru/eng/izv9081
  • https://doi.org/10.4213/im9081
  • http://mi.mathnet.ru/eng/izv/v85/i3/p73

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
    Number of views:
    This page:135
    References:7
    First page:13

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021