Timeline for Automorphisms of Compact Riemann Surfaces

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Dec 28, 2012 at 8:35	comment	added	roy smith		According to Serre, the precise result is essentially contained in Weil's proof, and I seem to recall a similarly precise statement in Matsusaka's paper on Torelli. So i would consult those sources. I have also been told that Torelli's original proof established a functor from Jacobians to curves, and Ciliberto has a more recent article (LNM 997) on Torelli type proofs, with inputs from Comessati that may shed some light.
Dec 28, 2012 at 8:09	comment	added	roy smith		it would take me some time to research this, but in principle i do not understand why any proof of Torelli would not yield the more precise result. although Serre says otherwise, e.g., of the Andreotti proof, it seems to me that an isomorphism of polarized Jacobians should yield an isomorphism of the dual curves and hence an isomorphism of curves. it remains of course to trace the composition of these functors to see that in one direction it yields an injection and in the other it equates isoms of Jac that are negatives of each other. Perhaps Serre or someone else will explain why not.
Dec 27, 2012 at 22:40	history	asked	user30246	CC BY-SA 3.0