π₁-small divisors and fundamental groups of varieties

2021/04/04 by Hao, Feng
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.01608

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 π₁(X) are finite. In this article, we generalize Lasell and Ramachandran's result to the case of π₁-small divisors on quasiprojective varieties. We also study π₁-small curves and hyperbolicity properties of smooth projective surfaces of general type with infinite fundamental groups.

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