Irreducibility of Lagrangian Quot schemes over an algebraic curve
Peer reviewed, Journal article
Published version
Date
2021-08-03Metadata
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Original version
https://doi.org/10.1007/s00209-021-02807-6Abstract
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.