Rational maps from products of curves to surfaces with p_g = q = 0

2021/11/16 by Nathan Chen, Olivier Martin, Chen, Nathan +1 · 1 citation
Mathematics · Social Sciences · #Algebraic Geometry and Number Theory #Vietnamese History and Culture Studies #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2111.08194

Abstract

We study dominant rational maps from a product of two curves to surfaces with p_g = q = 0. Given two curves which satisfy a mild genericity assumption and have large genus relative to their gonality, we show that the degree of irrationality of their product is equal to the product of their gonalities. Moreover, we prove that the degree of irrationality of a product of two hyperelliptic curves is 4.

Cited by

• A primer on measures of irrationality

Related

• On rational maps from the product of two general curves
• The Degree of Irrationality of del Pezzo Surfaces
• On rational maps from a general surface in P³ to surfaces of general type
• Pointless Hyperelliptic Curves
• Most hyperelliptic curves over Q have no rational points