11 papers
Rational homology disk degenerations of elliptic surfaces
Marcos Canedo, Giancarlo Urzúa
In this paper, a HD singularity is a weighted homogeneous normal surface singularity admitting a rational homology disk (HD) smoothing. These singularities…
Wahl singularities in degenerations of del Pezzo surfaces
Giancarlo Urzúa, Juan Pablo Zúñiga
For any fixed , we characterize all Wahl singularities that appear in degenerations of del Pezzo surfaces of degree . This extends the work of Manetti and…
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 . In this way, we identify all surfaces, smoothable or not, with only T-singul…
Tropical methods for stable octic double planes
Jonathan David Evans, Angelica Simonetti, Giancarlo Urzúa
This paper has been written to illustrate the power of techniques from tropical geometry and mirror symmetry for studying the KSBA moduli space of surfaces on or near the Noether l…
An exotic 5RP^2 in the 4-sphere
Gordana Matić, Ferit Öztürk, Javier Reyes +2
We show an example of an embedded copy of 5RP^2 in the four-sphere which is topologically standard but smoothly knotted, i.e. smoothly not isotopic to the standard embedding.
The birational geometry of Markov numbers
Giancarlo Urzúa, Juan Pablo Zúñiga
It is known that all degenerations of the complex projective plane into a surface with only quotient singularities are controlled by the positive integer solutions of the…
The Coble-Mukai lattice from -Gorenstein deformations
Giancarlo Urzúa
We show some geometric properties of Enriques surfaces via -Gorenstein smoothings of Coble surfaces. In particular, we explicitly identify the Enriques lattice of the ge…
Optimal bounds for many T-singularities in stable surfaces
Fernando Figueroa, Julie Rana, Giancarlo Urzúa
We effectively bound T-singularities on non-rational projective surfaces with an arbitrary amount of T-singularities and ample canonical class. This fully generalizes the previous…
Exotic surfaces
Javier Reyes, Giancarlo Urzúa
We construct the first exotic by means of rational blowdowns. Similarly, we construct the first exotic $3\mathbb C \ma…
Categorical aspects of the Kollár--Shepherd-Barron correspondence
Jenia Tevelev, Giancarlo Urzúa
It is well known that a -dimensional cyclic quotient singularity has the same singularity category as a finite dimensional associative algebra intr…
Rational configurations in K3 surfaces and simply-connected surfaces for
Javier Reyes, Giancarlo Urzúa
We prove the existence of -dimensional families of simply-connected surfaces with ample canonical class, , and , and we study the relation with…