Irreducibility of Lagrangian Quot schemes over an algebraic curve

On Punctual Quot Schemes for Algebraic Surfaces

Let S be a smooth projective surface over the field of complex numbers C. Fix a closed point s ∈ S and a pair of positive integers r, d. By results of Grothendieck (cf. [6], [11]) there exists a projective scheme Quot [s] (r, d) parametrizing all quotient sheaves O ⊕r S → A of length d supported at s. We consider this scheme with its reduced scheme structure and call it the punctual Quot scheme...

On the Cohomology of Brill-noether Loci over Quot Schemes

Let C be a smooth projective irreducible curve over an algebraic closed field k of characteristic 0. We consider Brill-Noether loci over the moduli space of morphisms from C to a Grassmannian G(m, n) of m−planes in k and the corresponding Quot schemes of quotients of a trivial vector bundle on C compactifying the spaces of morphisms. We study in detail the case in which m = 2, n = 4. We prove r...

On the Cohomology of Brill-noether Strata over Quot Schemes

We define a Brill-Noether stratification over the Quot scheme parametrizing quotients of a trivial bundle on a curve and we compute their cohomology classes.

Stable maps and Quot schemes

0 Stable maps and Quot schemes