Irreducibility of Lagrangian Quot schemes over an algebraic curve

Abstract

Let C be a complex projective smooth curve and W a symplectic vector bundle of rank 2n over C. The Lagrangian Quot scheme LQ_{−e}(W) parameterizes subsheaves of rank n and degree −e which are isotropic with respect to the symplectic form. We prove that LQ_{−e}(W) is irreducible and generically smooth of the expected dimension for all large e, and that a generic element is saturated and stable.