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arXiv · 2502.16742

Curve neighborhoods and combinatorial property $\mathcal{O}$ for a family of odd symplectic partial flag manifolds

Connor Bean·Bradley Cruikshank·Ryan M. Shifler
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Abstract

Let $E$ be an odd dimensional complex vector space and $\mbox{IF}:=\mbox{IF}(1,2;E)$ be the family of odd symplectic partial flag manifold. In this paper we give a full description of the irreducible components of the degree $d$ curve neighborhood of any Schubert variety of $\mbox{IF}$, study their lattice structure, and prove a combinatorial version of Conjecture $\mathcal{O}.$

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Connor Bean, Bradley Cruikshank, Ryan M. Shifler. 2025-02-23. Curve neighborhoods and combinatorial property $\mathcal{O}$ for a family of odd symplectic partial flag manifolds. https://arxiv.org/abs/2502.16742

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