Abstract:

This talk is mostly an introductory talk, that aims at conveying a basic understanding of Shimura varieties of orthogonal type (denoted by X) and certain subvarieties that are called "special cycles". We focus on the case of codimension 1 cycles, that is, on special divisors. Some of them, which are called principle special divisors, arise as divisors of meromorphic functions on X. Since the set of special divisors carries an abelean group structure, one can define abstract "divisor classes" by quotiening out principle ones. We will explain these notions, and indicate why they are important.

At the end of the talk, we will sketch an algorithm that enumerates all principle special divisors, and thus computes representatives of divisor classes.