Giancarlo Urz'ua

activity

20212025

collaborators

4 papers

math.AG2025

Wahl singularities in degenerations of del Pezzo surfaces

Giancarlo Urzúa, Juan Pablo Zúñiga

For any fixed $1 \leq ℓ \leq 9$ , we characterize all Wahl singularities that appear in degenerations of del Pezzo surfaces of degree $ℓ$ . This extends the work of Manetti and…

math.AG2024

Classification of Horikawa surfaces with T-singularities

Vicente Monreal, Jaime Negrete, Giancarlo Urzúa

We classify all projective surfaces with only T-singularities, ample canonical class, and $K^{2} = 2 p_{g} - 4$ . In this way, we identify all surfaces, smoothable or not, with only T-singul…

math.AG2022

Exotic surfaces

Javier Reyes, Giancarlo Urzúa

We construct the first exotic $C P^{2} #4 C P^{2}$ by means of rational blowdowns. Similarly, we construct the first exotic $3\mathbb C \ma…

math.AG2021

Rational configurations in K3 surfaces and simply-connected $p_{g} = 1$ surfaces for $K^{2} = 1, 2, 3, 4, 5, 6, 7, 8, 9$

Javier Reyes, Giancarlo Urzúa

We prove the existence of $(20 - 2 K^{2})$ -dimensional families of simply-connected surfaces with ample canonical class, $p_{g} = 1$ , and $1 \leq K^{2} \leq 9$ , and we study the relation with…

Wahl singularities in degenerations of del Pezzo surfaces

Classification of Horikawa surfaces with T-singularities

Exotic surfaces

Rational configurations in K3 surfaces and simply-connected pg​=1 surfaces for K2=1,2,3,4,5,6,7,8,9

Rational configurations in K3 surfaces and simply-connected $p_{g} = 1$ surfaces for $K^{2} = 1, 2, 3, 4, 5, 6, 7, 8, 9$