Found 2 relevant results in 1.63s where lecturer="Alessandro Giacchetto"
The course will be a first introduction to Riemann surfaces. These are beautiful objects that sit at the intersection of algebra, geometry, and analysis. We will aim to cover the theorems of Riemann–Hurwitz and Riemann–Roch, as well as the basics of Hurwitz theory. Time permitting, we may delve into additional subjects such as abelian integrals and the Abel–Jacobi theorem.
Toric varieties provide a rich class of examples in algebraic geometry that bridge combinatorics and geometry, making them an ideal starting point for exploring the interplay between these fields. We will introduce toric varieties, study their combinatorial and abstract structures, and examine their basic geometry, including singularities, Picard groups, and cohomology.