On some boundary divisors in the moduli spaces of stable Horikawa surfaces with K²=2p_g-3

2025/02/22 by Ciliberto, Ciro, Pardini, Rita
#14J10 #14J17 #14J29 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.16322

Abstract

We describe the normal stable surfaces with K²=2p_g-3 and p_g>14 whose only non canonical singularity is a cyclic quotient singularity of type 1/4k(1,2k-1) and the corresponding locus D inside the KSBA moduli space of stable surfaces. More precisely, we show that: (1) a general point of any irreducible component of D corresponds to a surface with a singularity of type 1/4(1,1), (2) the closure of D is a divisor contained in the closure of the Gieseker moduli space of canonical models of surfaces with K²=2p_g-3 and intersects all the components of such closure, and (3) the KSBA moduli space is smooth at a general point of D. In addition, we show that D has 1 or 2 irreducible components, depending on the residue class of p_g modulo 4.

Related

• Standard stable Horikawa surfaces
• Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces
• A boundary divisor in the moduli space of stable quintic surfaces
• I-surfaces with one T-singularity
• ℤ₃-actions on Horikawa surfaces