Foliations of algebraic varieties

Michael McQuillan (Rome Tor Vergata)

Monday 8th December 15:00-16:00
Maths 311B

Abstract

The division of Riemann surfaces afforded by the uniformisation theorem into those of constant positive, zero, or flat curvature is equally their division according to negative, 0, or positive Kodaira dimension. The habitual generalisation of this paradigm is the (ongoing) classification of algebraic varieties by their Kodaira dimension, but the same circle of ideas may equally be employed to holomorphic foliations wherein the classification of foliated surfaces, [1], is a rather tight generalisation of the uniformisation theorem, while the main open question in the classification of varieties, the existence of a minimal model, has a positive solution, [2], for foliations in Riemann surfaces in all dimensions.

[1] McQuillan, M. Canonical models of foliations, Pure and applied math quarterly, vol. 4, number 3, 877-1012, 2008.

[2] McQuillan, M. (2024). Semi-Stable Reduction of Foliations. In: Tschinkel, Y. (eds) Arithmetic and Algebraic Geometry. Simons Symposia. Springer, Cham.

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