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4 papers · 2 filters
The theta characteristic of a branched covering
Alex Eskin, Andrei Okounkov, Rahul Pandharipande
We give a group-theoretic description of the parity of a pull-back of a theta characteristic under a branched covering. It involves lifting monodromy of the covering to the semidir…
Planar dimers and Harnack curves
Richard Kenyon, Andrei Okounkov
In this paper we study the connection between dimers and Harnack curves discovered in math-ph/0311005. We prove that every Harnack curve arises as a spectral curve of some dimer mo…
Gradients of odd theta functions
Samuel Grushevsky, Riccardo Salvati Manni
We show that a generic principally polarized abelian variety (ppav) is uniquely determined by its theta hyperplanes. These are the non-projectivized version of those studied by Cap…
Virasoro constraints for target curves
Andrei Okounkov, Rahul Pandharipande
We prove generalized Virasoro constraints for the relative Gromov-Witten theories of all nonsingular target curves. Descendents of the even cohomology classes are studied first by…