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# Moduli of Rank 2 Stable Bundles and Hecke Curves

Published:2016-09-29
Printed: Dec 2016
• Sarbeswar Pal,
Indian Institute of Science Education and Research Thiruvananthapuram, Thiruvananthapuram-695016, India
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## Abstract

Let $X$ be smooth projective curve of arbitrary genus $g \gt 3$ over complex numbers. In this short note we will show that the moduli space of rank $2$ stable vector bundles with determinant isomorphic to $L_x$, where $L_x$ denote the line bundle corresponding to a point $x \in X$ is isomorphic to certain lines in the moduli space of S-equivalence classes of semistable bundles of rank 2 with trivial determinant.
 Keywords: Hecke curve, (0, 1) stable bundle
 MSC Classifications: 14D21 - Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx]

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