RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Model. Anal. Inform. Sist.:
Year:
Volume:
Issue:
Page:
Find






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


Model. Anal. Inform. Sist., 2015, Volume 22, Number 2, Pages 209–218 (Mi mais436)  

This article is cited in 1 scientific paper (total in 1 paper)

Uniformity of vector bundles of finite rank on complete intersections of finite codimension in a linear ind-Grassmannian

S. M. Yermakova

P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia

Abstract: A linear projective ind-variety $\mathbf X$ is called $1$-connected if any two points on it can be connected by a chain of lines $l_1, l_2,...,l_k$ in $\mathbf X$, such that $l_i$ intersects $l_{i+1}$. A linear projective ind-variety $\mathbf X$ is called $2$-connected if any point of $\mathbf X$ lies on a projective line in $\mathbf X$ and for any two lines $l$ and $l'$ in $\mathbf X$ there is a chain of lines $l=l_1, l_2,...,l_k=l'$, such that any pair $(l_i,l_{i+1})$ is contained in a projective plane $\mathbb P^2$ in $\mathbf X$.
In this work we study an ind-variety ${\mathbf X}$ that is a complete intersection in the linear ind-Grassmannian $\mathbf{G}=\underrightarrow{\lim}G(k_m,n_m)$. By definition, ${\mathbf X}$ is an intersection of ${\mathbf{G}}$ with a finite number of ind-hypersufaces $\mathbf{Y_i}=\underrightarrow{\lim}Y_{i,m}, {m\geq1}$, of fixed degrees $d_i$, $i=1,...,l$, in the space $\mathbf{P}^{\infty}$, in which the ind-Grassmannian $\mathbf{G}$ is embedded by Plücker.
One can deduce from work [17] that $\mathbf X$ is $1$-connected. Generalising this result we prove that $\mathbf X$ is $2$-connected. We deduce from this property that any vector bundle $\mathbf{E}$ of finite rank on $\mathbf X$ is uniform, i. e. the restriction of $\mathbf{E}$ to all projective lines in $\mathbf X$ has the same splitting type.
The motiavtion of this work is to extend theorems of Barth–Van de Ven–Tjurin–Sato type to complete intersections of finite codimension in ind-Grassmannians.

Full text: PDF file (515 kB)
References: PDF file   HTML file

Bibliographic databases:
UDC: 512.7
Received: 25.11.2014

Citation: S. M. Yermakova, “Uniformity of vector bundles of finite rank on complete intersections of finite codimension in a linear ind-Grassmannian”, Model. Anal. Inform. Sist., 22:2 (2015), 209–218

Citation in format AMSBIB
\Bibitem{Erm15}
\by S.~M.~Yermakova
\paper Uniformity of vector bundles of finite rank on complete intersections of~finite codimension in a linear ind-Grassmannian
\jour Model. Anal. Inform. Sist.
\yr 2015
\vol 22
\issue 2
\pages 209--218
\mathnet{http://mi.mathnet.ru/mais436}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3417822}
\elib{http://elibrary.ru/item.asp?id=23405829}


Linking options:
  • http://mi.mathnet.ru/eng/mais436
  • http://mi.mathnet.ru/eng/mais/v22/i2/p209

    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

    This publication is cited in the following articles:
    1. S. M. Ermakova, “Finite-Rank Vector Bundles on Complete Intersections of Finite Codimension in the Linear Ind-Grassmannian”, Math. Notes, 98:5 (2015), 852–856  mathnet  crossref  crossref  mathscinet  isi  elib
  • Моделирование и анализ информационных систем
    Number of views:
    This page:135
    Full text:40
    References:25

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020