The geometry of varieties

 Outline of the project

Geometry has evolved from the axiomatic approach of the ancient mathematicians to the modern study of complex and real spaces. Although this branch of Mathematics is commonly considered as a pure area, it has many applications in cryptography, coding theory, physics, differential equations, chemistry, among other areas. The scientific goal of this project is to understand of the geometry and symmetries of special algebraic varieties, in their many guises.

More concretely, this project intends to create new networks involving senior and young researchers and students, to strengthen collaboration and to create joint research in geometry and related topics by means of research activities and supporting the mobility of students and researchers in Chile, Brazil, Ecuador and France.

Research areas

• Riemann surfaces and their automorphisms

• Algebraic curves in positive characteristic

• Complex and arithmetical properties of rational maps

• Moduli spaces of sheaves

• Complex abelian varieties and Jacobians

• Qualitative study and analysis of partial differential equations

• Periods

• Geometry of moduli spaces of vector bundles over curves

• Algebraic groups in arithmetic, algebra and geometry

• The Riemann-Hilbert problem

• Prym-Tyurin varieties

Other Participating Institutions and Senior Researchers