Chennai Mathematical Institute


3.30 pm, Lecture Hall 5
Secant Bundles on Symmetric Powers of Curves

Krishanu Dan
Chennai Mathematical Institute.


Given a vector bundle on a irreducible, smooth, projective curve $C$ (over complex numbers), there is a naturally associated vector bundle on $S^n(C)$, the n-th symmetric power of $C$. This vector bundle was first introduced by R. Schwarzenberger, called it secant bundles. He used it to study the ring of rational equivalence class of $S^n(C)$. Secant bundle has natural parabolic structures. In this talk, we discuss the parabolic stability and Mumford-stability of this bundle. We will also mention some recent results regarding the stability of secant bundles (jointly with Suratno Basu).