论文标题
曲线正交捆绑包的各向同性引用方案
Isotropic Quot schemes of orthogonal bundles over a curve
论文作者
论文摘要
我们研究各向同性引号方案$ iq_e（v）$参数化度量$ e $ $ $ y $ y $ shosotropic子仓库的最大等级是曲线正交束$ v $的最大等级。方案$ iq_e（v）$包含空间的紧凑型$ iq^o_e（v）度的$ e $ e $ e $最大的各向同性分支，但行为与经典报价方案和[6]中的Lagrangian Quot Scheme的行为差异很大。我们观察到，对于某些拓扑类型的$ v $，计划$ iq_e（v）$对于所有$ e $都是空的。在其余的情况下，对于无限的许多$ e $，完全由不饱和子份额组成的$ iq_e（v）$的不可约组件，因此$ iq_e（v）$严格大于$ iq^o_e（v）$的$ iq_e（v）$。作为我们的主要结果，我们证明，对于任何正交包$ v $，对于$ e \ ll 0 $，closure $ \ overline {iq^o_e（v）$ of $ iq^o_e（v）$是空的，或者是一个或两个不可固定的连接组件，取决于$°（v）$ $ $。这样做，我们还表征了$ \ overline {iq^o_e（v）} $的不饱和部分时，$ v $甚至排名。
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 $e \ll 0$, the closure $\overline{IQ^o_e (V)}$ 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 $\overline{IQ^o_e (V)}$ when $V$ has even rank.
