Second order theta functions and vector bundles over Jacobi varieties

Yuen, David S.

doi:10.1090/S0002-9947-1990-1012508-7

Second order theta functions and vector bundles over Jacobi varieties
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by David S. Yuen PDF

Trans. Amer. Math. Soc. 320 (1990), 457-492 Request permission

Abstract:

We consider the Picard vector bundles defined over Jacobi varieties. The rank $g + 1$ Picard bundle imbeds in the rank ${2^g}$ Clifford bundle, so the second order theta functions, viewed appropriately, span the dual of the Picard bundle over each fiber. We prove a result on the minimum number of such second order theta functions required to span the whole bundle at each point. We give an application of using these functions to describe subvarieties of the Jacobian. There follow comments on which functions we could use, and generalizations to higher order theta functions.

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