Lectures

 

Vector bundles in Algebraic Geometry

Notas del curso.

Enrique Arrondo

Departamento de Ciencias Matemáticas
Universidad Complutense de Madrid

This introductory course will be mainly based on examples (hopefully complemented with more detailed theory notes by the teacher). We will show how vector bundles appear naturally when trying to patch together local equations of subvarieties. We will describe how vector bundles can produce maps to Grassmannians and use this relationship to give an introduction to Chern classes and the so-called Porteous formula.

Abelian Varieties, Prym-Tyurin varieties

Herbert Lange

Mathematisches Institut
Friedrich-Alexander-Universität Erlangen-Nürnberg

This course is supposed to be be an introduction into the theory of Prym-Tyurin varieties. First the relevant definitions and results on abelian varieties and their polarizations will be given. After defining Prym-Tyurin varieties in general, the first interesting case, namely classical Prym varieties will be studied. Then we give a method of construction of the more general varieties using correspondences. Finally as many examples as possible and in particular Tyurin's original examples will be explained.