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arXiv · 2104.01608

$\pi_1$-small divisors and fundamental groups of varieties

Feng Hao
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Abstract

Lasell and Ramachandran show that the existence of rational curves of positive self-intersection on a smooth projective surface $X$ implies that all the finite dimensional linear representations of the fundamental group $\pi_1(X)$ are finite. In this article, we generalize Lasell and Ramachandran's result to the case of $\pi_1$-small divisors on quasiprojective varieties. We also study $\pi_1$-small curves and hyperbolicity properties of smooth projective surfaces of general type with infinite fundamental groups.

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Feng Hao. 2021-04-04. $\pi_1$-small divisors and fundamental groups of varieties. https://arxiv.org/abs/2104.01608

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