Teaser for problem from hell

S is a symmetric nxn matix, L a line bundle on an abelian variety A, set 

\ L^S = \bigotimes_i p_i^*L^{s_{ii}} \bigotimes_{i<j} p_{ij}^*\Lambda(L)^{s_{ij}}

M is an mxn matrix so defines a map A^m —> A^n,  \ M^*L^S, \ L^{M^t S M} ahhhhh!

Simple enough to state but its an index nightmare!  I didn’t get to read more of Polishcuk, Hartshorne, or any other good reading because of this.  No summer project updates or HAPPY stuff.  Damn this problem.  More to come later…


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