Torsion on Jacobians and Teichmuller dynamics

In this post, I will describe a special case of a theorem about torsion points on Jacobians and Teichmuller dynamics which is proved in this paper. Namely, I will describe a different proof of a theorem of Moeller that for Teichmuller curves, zeroes of the holomorphic {1}-form must land in the torsion of (a factor of) the Jacobian. Some familiarity with Teichmuller dynamics will be assumed, as in the survey of Zorich.

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Grothendieck and the (generalized) Hodge conjecture

Grothendieck famously wrote a paper called Hodge’s general conjecture is false for trivial reasons. In this post, I would like to record, for my own benefit, some of the observations made in it.

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