Geometry

 

Integrability of Distributions Spanned

by Minimal Rational Tangents

Professor Ngaiming Mok
The University of Hong Kong

Abstract

The lecture is expository in nature and is accessible with a minimum background in Algebraic Geometry. For the purpose of studying deformation rigidity on Fano manifolds Jun-Muk Hwang and the author studied on a Fano manifold X minimal rational curves, their associated varieties of minimal rational tangents (i.e. tangents to minimal rational curves) and distributions W spanned by varieties of minimal rational tangents. Classically, integrability of distribution is checked using the Frobenius Theorem. For the distributions W we have obtained conditions which guarantee integrability formulated in terms of projective-geometric properties of varieties of minimal rational tangents Image39. Especially, using Zak’s Theorem on Tangencies, we show that W is integrable if a generic Image40 is non-singular, irreducible and dim Image41. This result is essential for the study of holomorphic vector fields on Fano manifolds.

 

Lecture I:

April 10, 2002 (Wed)

4:00pm

Lecture II:

April 19, 2002 (Fri)

4:00pm

Lecture III:

April 26, 2002 (Fri)

4:00pm

Lecture IV:

May 3, 2002 (Fri)

4:00pm

 

 

 

All are welcome