Nagoya Mathematical Journal

On the theta divisor of {${\rm SU}(r,1)$}

Sonia Brivio and Alessandro Verra

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Abstract

Let $SU(r,1)$ be the moduli space of stable vector bundles, on a smooth curve $C$ of genus $g \geq 2$, with rank $r \geq 3$ and determinant $O_C(p)$, $p \in C$; let ${\cal L}$ be the generalized theta divisor on $SU(r,1)$. In this paper we prove that the map ${\phi}_{\cal L}$, defined by ${\cal L}$, is a morphism and has degree $1$.

Article information

Source
Nagoya Math. J., Volume 165 (2002), 179-193.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631704

Mathematical Reviews number (MathSciNet)
MR1892104

Zentralblatt MATH identifier
1020.14011

Subjects
Primary: 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05]
Secondary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 14M20: Rational and unirational varieties [See also 14E08]

Citation

Brivio, Sonia; Verra, Alessandro. On the theta divisor of {${\rm SU}(r,1)$}. Nagoya Math. J. 165 (2002), 179--193. https://projecteuclid.org/euclid.nmj/1114631704


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