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 ©
 
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