Fundamental forms and infinitesimal symmetries of projective varieties

The fundamental form is a basic object for manifolds and varieties. In this talk, we will give a bound on the dimension of the linear automorphism group of a projective variety $Z \subset \mathbb{P} V$ in terms of its fundamental forms at a general point. Moreover, we will show that the bound is achieved precisely when $Z \subset \mathbb{P} V$ is projectively equivalent to an Euler-symmetric variety. The applications in the rigidity problem will also be discussed. This talk is based on a joint work with Jun-Muk Hwang.