Uniformity of Vector Bundles of Finite Rank on Complete Intersections of Finite Codimension in a Linear ind-Grassmannian
A linear projective ind-variety X is called 1-connected if any two points on it can be connected by a chain of lines l1, l2, ..., lk in X, such that li intersects li+1. A linear projective ind-variety X is called 2-connected if any point of X lies on a projective line in X and for any two lines l an...
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Yaroslavl State University
2015-04-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/241 |
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| author | S. M. Yermakova |
| author_facet | S. M. Yermakova |
| author_sort | S. M. Yermakova |
| collection | DOAJ |
| description | A linear projective ind-variety X is called 1-connected if any two points on it can be connected by a chain of lines l1, l2, ..., lk in X, such that li intersects li+1. A linear projective ind-variety X is called 2-connected if any point of X lies on a projective line in X and for any two lines l and l 0 in X there is a chain of lines l = l1, l2, ..., lk = l 0 , such that any pair (li , li+1) is contained in a projective plane P 2 in X. In this work we study an ind-variety X that is a complete intersection in the linear ind-Grassmannian G = lim−→G(km, nm). By definition, X is an intersection of G with a finite number of ind-hypersufaces Yi = lim−→Yi,m, m ≥ 1, of fixed degrees di , i = 1, ..., l, in the space P∞, in which the ind-Grassmannian G is embedded by Pl¨ucker. One can deduce from work [17] that X is 1-connected. Generalising this result we prove that X is 2-connected. We deduce from this property that any vector bundle E of finite rank on X is uniform, i. e. the restriction of E to all projective lines in 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. |
| format | Article |
| id | doaj-art-7fbf8eb3e5914c0ca82b20be098d10e9 |
| institution | DOAJ |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2015-04-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-7fbf8eb3e5914c0ca82b20be098d10e92025-08-20T03:01:13ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172015-04-0122220921810.18255/1818-1015-2015-2-209-218234Uniformity of Vector Bundles of Finite Rank on Complete Intersections of Finite Codimension in a Linear ind-GrassmannianS. M. Yermakova0P.G. Demidov Yaroslavl State UniversityA linear projective ind-variety X is called 1-connected if any two points on it can be connected by a chain of lines l1, l2, ..., lk in X, such that li intersects li+1. A linear projective ind-variety X is called 2-connected if any point of X lies on a projective line in X and for any two lines l and l 0 in X there is a chain of lines l = l1, l2, ..., lk = l 0 , such that any pair (li , li+1) is contained in a projective plane P 2 in X. In this work we study an ind-variety X that is a complete intersection in the linear ind-Grassmannian G = lim−→G(km, nm). By definition, X is an intersection of G with a finite number of ind-hypersufaces Yi = lim−→Yi,m, m ≥ 1, of fixed degrees di , i = 1, ..., l, in the space P∞, in which the ind-Grassmannian G is embedded by Pl¨ucker. One can deduce from work [17] that X is 1-connected. Generalising this result we prove that X is 2-connected. We deduce from this property that any vector bundle E of finite rank on X is uniform, i. e. the restriction of E to all projective lines in 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.https://www.mais-journal.ru/jour/article/view/241ind-grassmannianvector bundleuniform bundlefano variety of lines |
| spellingShingle | S. M. Yermakova Uniformity of Vector Bundles of Finite Rank on Complete Intersections of Finite Codimension in a Linear ind-Grassmannian Моделирование и анализ информационных систем ind-grassmannian vector bundle uniform bundle fano variety of lines |
| title | Uniformity of Vector Bundles of Finite Rank on Complete Intersections of Finite Codimension in a Linear ind-Grassmannian |
| title_full | Uniformity of Vector Bundles of Finite Rank on Complete Intersections of Finite Codimension in a Linear ind-Grassmannian |
| title_fullStr | Uniformity of Vector Bundles of Finite Rank on Complete Intersections of Finite Codimension in a Linear ind-Grassmannian |
| title_full_unstemmed | Uniformity of Vector Bundles of Finite Rank on Complete Intersections of Finite Codimension in a Linear ind-Grassmannian |
| title_short | Uniformity of Vector Bundles of Finite Rank on Complete Intersections of Finite Codimension in a Linear ind-Grassmannian |
| title_sort | uniformity of vector bundles of finite rank on complete intersections of finite codimension in a linear ind grassmannian |
| topic | ind-grassmannian vector bundle uniform bundle fano variety of lines |
| url | https://www.mais-journal.ru/jour/article/view/241 |
| work_keys_str_mv | AT smyermakova uniformityofvectorbundlesoffiniterankoncompleteintersectionsoffinitecodimensioninalinearindgrassmannian |