Featuring a mix of unique study papers and complete surveys from a global staff of prime researchers within the thriving fields of foliation idea, holomorphic foliations, and birational geometry, this publication provides the complaints of the convention "Foliation thought in Algebraic Geometry," hosted by means of the Simons beginning in ny urban in September 2013. 
Topics lined contain: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the constitution of symmetric differentials on a soft advanced floor and a neighborhood constitution theorem for closed symmetric differentials of rank ; an summary of lifting symmetric differentials from kinds with canonical singularities and the purposes to the class of AT bundles on singular forms; an outline of the robust thought of the diversity of minimum rational tangents brought via Hwang and Mok; contemporary examples of sorts that are hyperbolic and but the Green-Griffiths locus is the complete of X; and a class of psuedoeffective codimension one distributions.

Foliations play a primary position in algebraic geometry, for instance within the evidence of abundance for threefolds and to an answer of the Green-Griffiths conjecture for surfaces of basic variety with confident Segre classification. the aim of this quantity is to foster verbal exchange and let interactions among specialists who paintings on holomorphic foliations and birational geometry, and to assemble major researchers to illustrate the robust connection of rules, tools, and pursuits shared by way of those components of study.

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