Surfaces with c₁² =9 and χ=5 whose canonical classes are divisible by 3

2020/03/29 by Murakami, Masaaki
#14J29 (Primary ) 13J10 #32G05 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.12995

Abstract

We shall study minimal complex surfaces with c² = 9 and χ=5 whose canonical classes are divisible by 3 in the integral cohomology groups, where c₁² and χ denote the first Chern number of an algebraic surface and the Euler characteristic of the structure sheaf, respectively. The main results are a structure theorem for such surfaces, the unirationality of the moduli space, and a description of the behavior of the canonical map. As a byproduct, we shall also rule out a certain case mentioned in a paper by Ciliberto--Francia--Mendes Lopes. Since the irregularity q vanishes for our surfaces, our surfaces have geometric genus p_g = 4.

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