Chennai Mathematical Institute


Tuesday, December 1, 2020, 3:30 PM
Zoom Meeting Link:
Meeting ID: 859 2331 2360
Passcode: 392843
System of Hodge bundles and generalised Opers on smooth projective varieties

Suratno Basu
Chennai Mathematical Institute.


Let $k$ be an algebraically closed field of any characteristic. Let $X$ be a polarised smooth irreducible projective variety over $k$. A system of Hodge bundles is defined to be a Higgs bundle $(E,\theta)$ on $X$ such that $E=E_0\oplus ..\oplus E_n$ and the Higgs field $\theta$ satisfies $\theta(E_p)\subseteq E_{p-1}\otimes \Omega_{_X}^1$, $p=0,..,n$, where $\Omega_{_X}^1$ is the cotangent bundle. System of Hodge bundles naturally arise as $k^*$ fixed points of the moduli space of poly stable Higgs bundles. On the other hand given a vector bundle $F$ on $X$ together with a flat connection and a ''transversal filtration'' one can associate a system Hodge bundles. In this talk we discuss these notions and describe a semi stabiltiy criteria for system of Hodge bundles. We also give a very brief survey of the main result of an article by C.T Simpson which will clarify the importance of these objects.

This talk will be based on a joint work with Arjun Paul and Arideep Saha.