A Borel--Weil--Bott theorem for Quot schemes on ${\mathbb{P}}^1$

Ajay Gautam, Feiyang Lin, Shubham Sinha

We study the cohomology groups of tautological bundles on Quot schemes over the projective line, which parametrize rank $r$ quotients of a vector bundle $V$ on ${\mathbb{P}}^1$. Our…