Guolei Zhong, Positivity of Tangent Sheaf of Projective Varieties

In this talk, we discuss the structure of projective varieties with certain positive tangent sheaves. More precisely, when the tangent sheaf is almost nef or positively curved, we construct a well-defined MRC fibration and study the Fujita decomposition of reflexive sheaves. Besides, we show that the almost nefness of the tangent sheaf will impose rather restrictive condition on the singularities, and some typical examples will be given. This is based on my recent joint work with Masataka Iwai and Shin-ichi Matsumura.