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arXiv · 2104.03345

Restricted tangent bundles for general free rational curves

Brian Lehmann·Eric Riedl
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Abstract

Suppose that $X$ is a smooth projective variety and that $C$ is a general member of a family of free rational curves on $X$. We prove several statements showing that the Harder-Narasimhan filtration of $T_{X}|_{C}$ is approximately the same as the restriction of the Harder-Narasimhan filtration of $T_{X}$ with respect to the class of $C$. When $X$ is a Fano variety, we prove that the set of all restricted tangent bundles for general free rational curves is controlled by a finite set of data. We then apply our work to analyze Peyre's "freeness" formulation of Manin's Conjecture in the setting of rational curves.

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Brian Lehmann, Eric Riedl. 2021-04-07. Restricted tangent bundles for general free rational curves. https://arxiv.org/abs/2104.03345

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