| Title:
|
Infinite-dimensional complex projective spaces and complete intersections (English) |
| Author:
|
Ballico, E. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
131 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
419-425 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $V$ be an infinite-dimensional complex Banach space and $X \subset {\mathbf {P}}(V)$ a closed analytic subset with finite codimension. We give a condition on $X$ which implies that $X$ is a complete intersection. We conjecture that the result should be true for more general topological vector spaces. (English) |
| Keyword:
|
infinite-dimensional complex projective space |
| Keyword:
|
infinite-dimensional complex manifold |
| Keyword:
|
complete intersection |
| Keyword:
|
complex Banach space |
| Keyword:
|
complex Banach manifold |
| MSC:
|
32K05 |
| MSC:
|
58B20 |
| idZBL:
|
Zbl 1109.32015 |
| idMR:
|
MR2273932 |
| DOI:
|
10.21136/MB.2006.133969 |
| . |
| Date available:
|
2009-09-24T22:28:03Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133969 |
| . |
| Reference:
|
[1] B. Kotzev: Vanishing of the first cohomology group of line bundles on complete intersections in infinite-dimensional projective space.Ph.D. thesis, University of Purdue, 2001. MR 2704133 |
| Reference:
|
[2] L. Lempert: The Dolbeaut complex in infinite dimension.J. Amer. Math. Soc. 11 (1998), 485–520. MR 1603858, 10.1090/S0894-0347-98-00266-5 |
| Reference:
|
[3] A. N. Tyurin: Vector bundles of finite rank over infinite varieties.Math. USSR Izvestija 10 (1976), 1187–1204. 10.1070/IM1976v010n06ABEH001832 |
| . |
