关于$\mathbb{P}^2$上的两个向量束的不变秩

Pub Date : 2020-10-13 DOI:10.5565/publmat6712306

Simone Marchesi, J. Vallès

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摘要

本文刻画了在投影平面上固定点的Gp:= Stabp(PGL(3))、固定直线的GL:= StabL(PGL(3))和T = Gp∩GL作用下p2上的两个秩向量束的不变性，并且证明了由不变性引起的跳跃轨迹的几何构型并不表征不变性本身。事实上，我们发现有无限个族几乎是均匀的，但不是均匀的。

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On invariant rank two vector bundles on $\mathbb{P}^2$

In this paper we characterize the rank two vector bundles on P 2 which are invariant under the action of Gp := Stabp(PGL(3)), that fixes a point in the projective plane, GL := StabL(PGL(3)), that fixes a line, and T = Gp ∩ GL. Moreover, we prove that the geometrical configuration of the jumping locus induced by the invariance does not, on the other hand, characterize the invariance itself. Indeed, we find infinity families that are almost uniform but not almost homogeneous.

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