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arXiv · 1804.00052

Irreducibility of Lagrangian Quot schemes over an algebraic curve

Daewoong Cheong·Insong Choe·George H. Hitching
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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.

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Daewoong Cheong, Insong Choe, George H. Hitching. 2018-03-30. Irreducibility of Lagrangian Quot schemes over an algebraic curve. https://arxiv.org/abs/1804.00052

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