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Spin Verlinde Spaces and Prym Theta Functions
Author(s) -
Oxbury W. M.
Publication year - 1999
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611599001665
Subject(s) - pfaffian , mathematics , moduli space , line bundle , bundle , pure mathematics , algebraic curve , spin (aerodynamics) , product (mathematics) , theta function , line (geometry) , space (punctuation) , moduli , mathematical analysis , geometry , physics , quantum mechanics , linguistics , philosophy , materials science , composite material , thermodynamics
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. 1991 Mathematics Subject Classification : 14D20, 14H42, 14H60, 14K25.