Seminars

 Tuesday, December 1, 2020, 3:30 PM Zoom Meeting Link: https://us02web.zoom.us/j/85923312360?pwd=aFk5R2Z1alJ6dEV0UlBHQkV2aU84dz09 Meeting ID: 859 2331 2360 Passcode: 392843 System of Hodge bundles and generalised Opers on smooth projective varieties Suratno Basu Chennai Mathematical Institute. 01-12-20 Abstract 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.