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arXiv · 1701.08242

A note on the codimension of the linear section of the Lagrangian-Grassmannian L(6,12)

Jesús Carrillo-Pacheco·Fausto Jarquín-Zárate·Maurilio Velasco-Fuentes·Felipe Zaldívar
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Abstract

Consider a $2n$-dimensional symplectic vector space $E$ over an arbitrary field $\mathbb{F}$. Given a contraction map $f: \wedge^n E \rightarrow \wedge^{n-2} E$ such that the Lagrangian--Grassmannian $L(n,2n)=G(n,2n)\cap{\mathbb P}(\ker f)$, where $\wedge^r E$ denotes the $r$-th exterior power of $E$ and ${\mathbb P}(\ker f)$ is the projectivization of $\ker f$. In this paper, for a symplectic vector space $E$ of dimension $n=6$, we prove that the surjectivity of the contraction map $f:\wedge^{6} E \rightarrow \wedge^{4} E$ depends on the characteristic of the base field and we calculate the codimension of the linear section ${\mathbb P}(\ker f)\subseteq {\mathbb P}(\wedge^{6}E)$ for any characteristic.

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Jesús Carrillo-Pacheco, Fausto Jarquín-Zárate, Maurilio Velasco-Fuentes, Felipe Zaldívar. 2017-01-28. A note on the codimension of the linear section of the Lagrangian-Grassmannian L(6,12). https://arxiv.org/abs/1701.08242

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