Isotropic Quot schemes of orthogonal bundles over a curve

2020/06/16 by Cheong, Daewoong, Choe, Insong, Hitching, George H. · 2 citations
#14H60 #14M17 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.09528

Abstract

We study the isotropic Quot schemes IQ_e (V) parameterizing degree e isotropic subsheaves of maximal rank of an orthogonal bundle V over a curve. The scheme IQ_e (V) contains a compactification of the space IQ^o_e (V) of degree e maximal isotropic subbundles, but behaves quite differently from the classical Quot scheme, and the Lagrangian Quot scheme in [6]. We observe that for certain topological types of V, the scheme IQ_e (V) is empty for all e. In the remaining cases, for infinitely many e there are irreducible components of IQ_e (V) consisting entirely of nonsaturated subsheaves, and so IQ_e (V) is strictly larger than the closure of IQ^o_e (V). As our main result, we prove that for any orthogonal bundle V and for e ≪ 0, the closure IQ^o_e (V) of IQ^o_e (V) is either empty or consists of one or two irreducible connected components, depending on °(V) and e. In so doing, we also characterize the nonsaturated part of IQ^o_e (V) when V has even rank.

Cited by

• On Vanishing of Gromov--Witten Invariants
• A short way of counting maps to hypersurfaces in Grassmannians

Related

• Counting maximal isotropic subbundles of orthogonal bundles over a curve
• The virtual intersection theory of isotropic Quot Schemes
• Low rank orthogonal bundles and quadric fibrations
• Irreducibility of Lagrangian Quot schemes over an algebraic curve
• Lagrangian subbundles of orthogonal bundles of odd rank over an algebraic curve