Holomorphic Foliations

Prerequisites: Introduction to Holomorphic Foliations and Riemann Surfaces (can be attended in parallel)

Line bundles and divisors. Intersection in surfaces. Line bundles associated to foliations, intersection formulas, index theorems, applications. Separatrix theorem. Riccati foliations and turbulent foliations. Realization of monodromy. Logarithmic forms and vector fields. Jouanolou theorem.
Classification of holomorphic vector fields on projective surfaces, Introduction to the birational theory (minimal models, Kodaira dimension). Applications.

References:
BRUNELLA, M. – Birational geometry of foliations. Publicações Matemáticas do IMPA. Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2004.
GÓMEZ-MONT, X., ORTÍZ-BOBADILLA, L. – Sistemas dinâmicos holomorfos em superfícies. México: Sociedad Matemática Mexicana, 1989.

* Standard program. The teacher has the autonomy to make any changes