On some boundary divisors in the moduli spaces of stable Horikawa surfaces with $K^2=2p_g-3$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910841010388992 |
|---|---|
| author | Ciliberto, Ciro Pardini, Rita |
| author_facet | Ciliberto, Ciro Pardini, Rita |
| contents | We describe the normal stable surfaces with K^2=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 K^2=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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16322 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On some boundary divisors in the moduli spaces of stable Horikawa surfaces with $K^2=2p_g-3$ Ciliberto, Ciro Pardini, Rita Algebraic Geometry 14J10, 14J17, 14J29 We describe the normal stable surfaces with K^2=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 K^2=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. |
| title | On some boundary divisors in the moduli spaces of stable Horikawa surfaces with $K^2=2p_g-3$ |
| topic | Algebraic Geometry 14J10, 14J17, 14J29 |
| url | https://arxiv.org/abs/2502.16322 |