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Transactions of the American Mathematical Society

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Differential operators on a polarized abelian variety

Author: Indranil Biswas
Journal: Trans. Amer. Math. Soc. 354 (2002), 3883-3891
MSC (2000): Primary 14K25, 14D20, 14H40
Published electronically: June 4, 2002
MathSciNet review: 1926857
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Abstract: Let $L$ be an ample line bundle over a complex abelian variety $A$. We show that the space of all global sections over $A$of ${Diff}^{n}_A(L,L)$ and $S^n({Diff}^1_A(L,L))$are both of dimension one. Using this it is shown that the moduli space $M_X$ of rank one holomorphic connections on a compact Riemann surface $X$ does not admit any nonconstant algebraic function. On the other hand, $M_X$ is biholomorphic to the moduli space of characters of $X$, which is an affine variety. So $M_X$ is algebraically distinct from the character variety if $X$ is of genus at least one.

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Additional Information

Indranil Biswas
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

Keywords: Abelian variety, differential operator, connection, representation space
Received by editor(s): April 5, 2001
Received by editor(s) in revised form: February 5, 2002
Published electronically: June 4, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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