Extension Groups of Tautological Bundles on Punctual Quot Schemes of Curves

Abstract: We prove formulas for the cohomology and the extension groups of tautological bundles on punctual Quot schemes over complex smooth projective curves. As a corollary, we show that the tautological bundle determines the isomorphism class of the original vector bundle on the curve. We also give a vanishing result for the push-forward along the Quot--Chow morphism of tensor and wedge products of duals of tautological bundles.