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arXiv · 2106.03123

The $\theta$-density in Arakelov geometry

Xiaozong Wang
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Abstract

In this article, we construct a $\theta$-density for the global sections of ample Hermitian line bundles on a projective arithmetic variety. We show that this density has similar behaviour to the usual density in the Arakelov geometric setting, where only global sections of norm smaller than $1$ are considered. In particular, we prove the analogue by $\theta$-density of two Bertini kind theorems, on irreducibility and regularity respectively.

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Xiaozong Wang. 2021-06-06. The $\theta$-density in Arakelov geometry. https://arxiv.org/abs/2106.03123

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