[HG_AG] Introduction to the positivity of tangent sheaves of projective varieties
ABSTRACT
After Mori's solution to the Hartshorne conjecture, it has become evident that a certain positivity condition of the tangent bundle would produce rich geometry on the underlying variety. Considering the minimal model program for the classification of algebraic varieties, the appearance of singularities is indispensable. In this talk, I will first briefly recall various notions on the positivity of tangent sheaves in the singular setting. Then we compare them with the classical notions in the smooth case and some pathological examples will be given. Finally, after a review of previous results in this direction, we state our main theorem on the structure of projective varieties with certain positive tangent sheaves. This talk is based on the joint work with Masataka Iwai and Shin-ichi Matsumura.