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

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 Differential operators and flat connections on a Riemann surface

2003 ◽  
Vol 2003 (64) ◽  
pp. 4041-4056
Author(s):  
Indranil Biswas
Keyword(s):  
Riemann Surface ◽  
Vector Bundle ◽  
Vector Bundles ◽  
Differential Operators ◽  
Transversality Condition ◽  
Jet Bundle ◽  
Holomorphic Differential ◽  
Isomorphism Classes ◽  
Holomorphic Vector Bundles ◽  
Natural Filtration

We consider filtered holomorphic vector bundles on a compact Riemann surfaceXequipped with a holomorphic connection satisfying a certain transversality condition with respect to the filtration. IfQis a stable vector bundle of rankrand degree(1−genus(X))nr, then any holomorphic connection on the jet bundleJn(Q)satisfies this transversality condition for the natural filtration ofJn(Q)defined by projections to lower-order jets. The vector bundleJn(Q)admits holomorphic connection. The main result is the construction of a bijective correspondence between the space of all equivalence classes of holomorphic vector bundles onXwith a filtration of lengthntogether with a holomorphic connection satisfying the transversality condition and the space of all isomorphism classes of holomorphic differential operators of ordernwhose symbol is the identity map.

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 $M$.

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.

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
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