Moduli of Vector Bundles on a Compact Riemann Surface

1969 ◽  
Vol 89 (1) ◽  
pp. 14 ◽  
Author(s):  
M. S. Narasimhan ◽  
S. Ramanan
Keyword(s):  
Riemann Surface ◽  
Vector Bundles ◽  
Compact Riemann Surface ◽  
Moduli Of Vector Bundles

Stable and Unitary Vector Bundles on a Compact Riemann Surface

1965 ◽  
Vol 82 (3) ◽  
pp. 540 ◽  
Author(s):  
M. S. Narasimhan ◽  
C. S. Seshadri
Keyword(s):  
Riemann Surface ◽  
Vector Bundles ◽  
Compact Riemann Surface

scholarly journals Moduli of endomorphisms of semistable vector bundles over a compact Riemann surface

1990 ◽  
Vol 32 (1) ◽  
pp. 1-12 ◽  
Author(s):  
L. Brambila Paz
Keyword(s):  
Riemann Surface ◽  
Vector Bundles ◽  
Compact Riemann Surface ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Finite Dimensional ◽  
Semistable Vector Bundles

Mumford and Suominen in [8] and Newstead in [11] have considered the moduli problem of classifying the endomorphisms of finite-dimensional vector spaces. Using similar ideas we consider the moduli problem for endomorphisms of indecomposable semistable vector bundles over a compact connected Riemann surface of genus g ≥ 2.

scholarly journals UNIQUENESS OF AFFINE STRUCTURES ON RIEMANN SURFACES

1992 ◽  
Vol 23 (2) ◽  
pp. 87-94
Author(s):  
JOHN T. MASTERSON
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Vector Bundles ◽  
Compact Riemann Surface ◽  
Single Point ◽  
Related Result ◽  
Low Degree ◽  
Affine Structures

Let $M$ be any compact Riemann surface of genus $g\ge 2$. It is first established that there do not exist on $M$ any generic low- degree simple polar variations of branched affine structures having fixed nonpolar and polar branch data and fixed induced character homomorphism $\tilde \psi$. Hence, these structures depend uniquely on the branch data and the homomorphism. A related result is also established concern­ing the nonexistence on $M$ of generic low-degree single-point variations of branched affine structures having fixed homomorphism $\tilde \psi$. These resuits depend on the Noether and Weierstrass gaps on $M$. Corollaries are derived concerning mappings induced by sections of vector bundles of affine structures and concerning structures on an arbitrary hyperelliptic or elliptic ($g =1$) surface $M$.

Holomorphic vector bundles on a compact Riemann surface

1964 ◽  
Vol 155 (1) ◽  
pp. 69-80 ◽  
Author(s):  
M. S. Narasimhan ◽  
C. S. Seshadri
Keyword(s):  
Riemann Surface ◽  
Vector Bundles ◽  
Compact Riemann Surface ◽  
Holomorphic Vector Bundles

scholarly journals Non-flat extension of flat vector bundles

2015 ◽  
Vol 26 (14) ◽  
pp. 1550114
Author(s):  
Indranil Biswas ◽  
Viktoria Heu
Keyword(s):  
Riemann Surface ◽  
Vector Bundle ◽  
Vector Bundles ◽  
Compact Riemann Surface ◽  
Holomorphic Vector Bundle ◽  
Flat Extension

We construct a pair [Formula: see text], where [Formula: see text] is a holomorphic vector bundle over a compact Riemann surface and [Formula: see text] a holomorphic subbundle, such that both [Formula: see text] and [Formula: see text] admit holomorphic connections, but [Formula: see text] does not.

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