Geodesic
On the Image of Certain Extension Maps. I
Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 427-433

Voir la notice de l'article provenant de la source Cambridge University Press

Let $X$ be a smooth complex projective curve of genus $g\ge 1$ . Let $\xi \in {{J}^{1}}\left( X \right)$ be a line bundle on $X$ of degree 1. Let $W=\text{Ex}{{\text{t}}^{1}}\left( {{\xi }^{n}},{{\xi }^{-1}} \right)$ be the space of extensions of ${{\xi }^{n}}$ by ${{\xi }^{-1}}$ . There is a rational map ${{D}_{\xi }}:G\left( n,W \right)\to S{{U}_{X}}\left( n+1 \right)$ , where $G\left( n,W \right)$ is the Grassmannian variety of $n$ -linear subspaces of $W$ and $S{{U}_{X}}\left( n+1 \right)$ is the moduli space of rank $n+1$ semi-stable vector bundles on $X$ with trivial determinant. We prove that if $n=2$ , then ${{D}_{\xi }}$ is everywhere defined and is injective.
DOI : 10.4153/CMB-2007-041-0
Mots-clés : 14H60, 14F05, 14D20 
Mejía, Israel Moreno. On the Image of Certain Extension Maps. I. Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 427-433. doi: 10.4153/CMB-2007-041-0
@article{10_4153_CMB_2007_041_0,
     author = {Mej{\'\i}a, Israel Moreno},
     title = {On the {Image} of {Certain} {Extension} {Maps.} {I}},
     journal = {Canadian mathematical bulletin},
     pages = {427--433},
     year = {2007},
     volume = {50},
     number = {3},
     doi = {10.4153/CMB-2007-041-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-041-0/}
}
TY  - JOUR
AU  - Mejía, Israel Moreno
TI  - On the Image of Certain Extension Maps. I
JO  - Canadian mathematical bulletin
PY  - 2007
SP  - 427
EP  - 433
VL  - 50
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-041-0/
DO  - 10.4153/CMB-2007-041-0
ID  - 10_4153_CMB_2007_041_0
ER  - 
%0 Journal Article
%A Mejía, Israel Moreno
%T On the Image of Certain Extension Maps. I
%J Canadian mathematical bulletin
%D 2007
%P 427-433
%V 50
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-041-0/
%R 10.4153/CMB-2007-041-0
%F 10_4153_CMB_2007_041_0

[1] [1] Atiyah, M. F.. Complex analytic connections in fibre bundles. Trans. Amer. Math. Soc. 85(1957), 181–207. Google Scholar

[2] [2] Brambila-Paz, L., Grzegorczyk, I., and Newstead, P. E., Geography of Brill-Noether loci for small slopes. J. Algebraic Geom. 6(1997), no. 4, 645–669. Google Scholar

[3] [3] Benson, D. J.. Representations and Cohomology. I. Second edition. Cambridge Studies in Advanced Mathematics 30, Cambridge University Press, Cambridge, 1998. Google Scholar

[4] [4] Bertram, A., Moduli of rank-2 vector bundles, theta divisors, and the geometry of curves in projective space. J. Differential Geom. 35(1992), no. 2, 429–469. Google Scholar

[5] [5] Lange, H. and Narasimhan, M. S.. Maximal subbundles of rank two vector bundles on curves. Math. Ann. 266(1983), no. 1, 55–72. Google Scholar

[6] [6] Le Potier, J.. Lectures on Vector Bundles. Cambridge Studies in Advanced Mathematics 54, Cambridge University Press, Cambridge, 1997. Google Scholar

[7] [7] Narasimhan, M. S. and Ramanan, S.. Moduli of vector bundles on a compact Riemann surface. Ann. of Math. 89(1969) 14–51. Google Scholar

[8] [8] Narasimhan, M. S. and Seshadri, C. S., Stable and unitary vector bundles on a compact Riemann surface. Ann. of Math. 82(1965), 540–567. Google Scholar

[9] [9] Seshadri, C. S., Space of unitary vector bundles on a compact Riemann surface. Ann. of Math. 85(1967), 303–336. Google Scholar

Cité par Sources :