Configuration spaces of algebraic varieties

Specialeforsvar: Mathias Nisted Velling

Titel: Configuration spaces of algebraic varieties

Resume: This thesis deals with a computer implementation of a spectral sequence by Totaro that can be used for the calculation of the rational cohomology of the configuration space $F(X,n)$ of ordered $n$-tuples of points in a smooth complex projective curve $X$ of genus $g$. The first chapter of the thesis introduces some theoretical prerequisites for the implementation. Section 1 introduces some basic algebraic objects used in the thesis. Section 2 introduces cohomology of spaces and the added algebraic structure coming from the cup product. Section 3 introduces manifolds and some cohomological properties of orientable manifolds. Section 4 briefly introduces spectral sequnces and section 5 deals with complex algebraic varieties, and finally section 6 briefly sums up the results of Totaro's paper. Chapter 2 contains the implementation details of the program. Section 1 contains details for the bases of the underlying algebras of the $E_2$-page of Totaro's spectral sequence. Section 2 contains details for operations with elements in these
algebras and section 3 contains details for the differential of the spectral sequence and calculating cohomology of the algebra. Appendix A contains a few example outputs from the implementation.

Vejleder: Dan Erik Petersen
Censor: John Olsen