2002/10/30 by Andrey N. Tyurin, Tyurin, Andrey N. · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.math/0210466
To Igor Rostislavovich Shafarevich on his 80th birthday (will be published by CRS, Canada)
arxiv created 2002/10/30 · arxiv updated 2009/11/30
In the abelian case (the subject of several beautiful books) fixing some combinatorial structure (so called theta structure of level k) one obtains a special basis in the space of sections of canonical polarization powers over the jacobians. These sections can be presented as holomorphic functions on the "abelian Schottky space". This fact provides various applications of these concrete analytic formulas to the integrable systems, classical mechanics and PDE's. Our practical goal is to do the same in the non abelian case that is to give an answer to the Beauville's question. In future we hope to extend this digest to a mathematical mohograph with title "VBAC".