Positivity and algebraic integrability of holomorphic foliations – Carolina Araujo – ICM2018 скачать в хорошем качестве

Positivity and algebraic integrability of holomorphic foliations – Carolina Araujo – ICM2018

Algebraic and Complex Geometry Invited Lecture 4.7 Positivity and algebraic integrability of holomorphic foliations Carolina Araujo Abstract: The theory of holomorphic foliations has its origins in the study of differential equations on the complex plane, and has turned into a powerful tool in algebraic geometry. One of the fundamental problems in the theory is to find conditions that guarantee that the leaves of a holomorphic foliation are algebraic. These correspond to algebraic solutions of differential equations. In this paper we discuss algebraic integrability criteria for holomorphic foliations in terms of positivity of its tangent sheaf, and survey the theory of Fano foliations, developed in a series of papers in collaboration with Stéphane Druel. We end by classifying all possible leaves of del Pezzo foliations. ICM 2018 – International Congress of Mathematicians © www.icm2018.org     Os direitos sobre todo o material deste canal pertencem ao Instituto de Matemática Pura e Aplicada, sendo vedada a utilização total ou parcial do conteúdo sem autorização prévia e por escrito do referido titular, salvo nas hipóteses previstas na legislação vigente. The rights over all the material in this channel belong to the Instituto de Matemática Pura e Aplicada, and it is forbidden to use all or part of it without prior written authorization from the above mentioned holder, except in the cases prescribed in the current legislation.