Surjective rational maps and del Pezzo surfaces

2023/11/03 by Karzhemanov, Ilya, Lekontseva, Anna
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.01835

Abstract

We study surjective (not necessarily regular) rational endomorphisms f of smooth del Pezzo surfaces X. We prove that under certain natural non - degeneracy condition f can have degree bigger than 1 only when (-K_X²) > 5. Some structural properties of f in the case X = \p² are also established.

Related

• Endomorphisms of singular del Pezzo surfaces
• Rational curves on del Pezzo surfaces in positive characteristic
• Rational points on certain del Pezzo surfaces of degree one
• Quotients of del Pezzo surfaces of high degree
• Rational Points on Del Pezzo Surface of degree 1 and 2