Lower bounds for genera of fiber products

2022/01/20 by Pakovich, Fedor · 2 citations
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2201.08231

Abstract

We give lower bounds for genera of components of fiber products of holomorphic maps between compact Riemann surfaces, extending results on genera of components of algebraic curves of the form A(x)-B(y)=0, where A and B are rational functions.

Cited by

• Holomorphic maps sharing preimages over finitely generated fields
• Periodic curves for general endomorphisms of \mathbb C\mathbb P¹× \mathbb C\mathbb P¹

Related

• On the fiber product over infinite-genus Riemann surfaces
• On the fiber product of Riemann surfaces
• Rational maps from products of curves to surfaces with p_g = q = 0
• Co-fibered products of algebraic curves
• Hurwitz existence problem and fiber products