SPIN VERLINDE SPACES AND PRYM THETA FUNCTIONS
1999 ◽
Vol 78
(1)
◽
pp. 52-76
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Keyword(s):
It is shown that the theta functions of level $n$ on the principally polarised Prym varieties of an algebraic curve are dual to the sections of the orthogonal theta line bundle on the moduli space of Spin($n$)-bundles over the curve. As a by-product of our computations, we also note that when $n$ is odd, the Pfaffian line bundle on moduli space has a basis of sections labelled by the even theta characteristics of the curve.