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arXiv · 1903.04238

Counting maximal Lagrangian subbundles over an algebraic curve

Daewoong Cheong·Insong Choe·George H. Hitching
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Abstract

Let $C$ be a smooth projective curve and $W$ a symplectic bundle over $C$. Let $LQ_e (W)$ be the Lagrangian Quot scheme parametrizing Lagrangian subsheaves $E \subset W$ of degree $e$. We give a closed formula for intersection numbers on $LQ_e (W)$. As a special case, for $g \ge 2$, we compute the number of Lagrangian subbundles of maximal degree of a general stable symplectic bundle, when this is finite. This is a symplectic analogue of Holla's enumeration of maximal subbundles in [13].

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Daewoong Cheong, Insong Choe, George H. Hitching. 2019-03-11. Counting maximal Lagrangian subbundles over an algebraic curve. https://arxiv.org/abs/1903.04238

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