4 citations · 9 across the 10 of their papers we have counts for
18 papers
On wormholes in the moduli space of surfaces
Giancarlo Urzúa, Nicolás Vilches
We study a certain wormholing phenomenon that takes place in the Kollár--Shepherd-Barron--Alexeev (KSBA) compactification of the moduli space of surfaces of general type. It occurs…
Chilean configuration of conics, lines and points
Igor Dolgachev, Antonio Laface, Ulf Persson +1
Using the theory of rational elliptic fibrations, we construct and discuss a one parameter family of configurations of conics and points in the projective plane that reali…
On degenerations of -Godeaux surfaces
Eduardo Dias, Carlos Rito, Giancarlo Urzúa
We compute equations for Coughlan's family of Godeaux surfaces with torsion , which we call -Godeaux surfaces, and we show that it is (at most) 7 dimensio…
Bounding tangencies of sections on elliptic surfaces
Douglas Ulmer, Giancarlo Urzúa
Given an elliptic surface over a field of characteristic zero equipped with zero section and another section of infinite order, we give a si…
Savage Surfaces
Sergio Troncoso, Giancarlo Urzúa
Let be the topological fundamental group of a given nonsingular complex projective surface. We prove that the Chern slopes of minimal nonsingular projective s…
Rigid surfaces arbitrarily close to the Bogomolov--Miyaoka--Yau line
Matthew Stover, Giancarlo Urzúa
We prove the existence of rigid compact complex surfaces of general type whose Chern slopes are arbitrarily close to the Bogomolov--Miyaoka--Yau bound of . In addition, each of…
Transversality of sections on elliptic surfaces with applications to elliptic divisibility sequences and geography of surfaces
Douglas Ulmer, Giancarlo Urzúa
We consider elliptic surfaces over a field equipped with zero section and another section of infinite order. If has characteristic zero, we show there…
Simple embeddings of rational homology balls and antiflips
Heesang Park, Dongsoo Shin, Giancarlo Urzúa
Let be a regular neighborhood of a negative chain of -spheres (i.e. exceptional divisor of a cyclic quotient singularity), and let be a rational homology ball whic…
Antiflips, mutations, and unbounded symplectic embeddings of rational homology balls
Jonathan David Evans, Giancarlo Urzúa
The Milnor fibre of a -Gorenstein smoothing of a Wahl singularity is a rational homology ball . For a canonically polarised surface of general type , it is…
On the geography of line arrangements
Sebastian Eterović, Fernando Figueroa, Giancarlo Urzúa
This is a short note on various results about the combinatorial properties of line arrangements in terms of the Chern numbers of the corresponding log surfaces. This resembles the…
Families of explicit quasi-hyperbolic and hyperbolic surfaces
Natalia Garcia-Fritz, Giancarlo Urzúa
We construct explicit families of quasi-hyperbolic and hyperbolic surfaces. This is based on earlier work of Vojta, and the recent expansion and generalization of it by the first a…
Optimal bounds for T-singularities in stable surfaces
Julie Rana, Giancarlo Urzúa
We explicitly bound T-singularities on normal projective surfaces with one singularity, and ample. This bound depends only on , and it is optimal when is not r…
Characterization of Kollár surfaces
Giancarlo Urzúa, José Ignacio Yáñez
Kollár introduced in [Ko08] the surfaces where , $W_i=a_{i+1}a_{i+2}a_{i…
On Z/3-Godeaux surfaces
Stephen Coughlan, Giancarlo Urzúa
We prove that Godeaux--Reid surfaces with torsion group Z/3 have topological fundamental group Z/3. For this purpose, we describe degenerations to stable KSBA surfaces with one 1/4…
Chern slopes of surfaces of general type in positive characteristic
Rodrigo Codorniu, Giancarlo Urzúa
Let be an algebraically closed field of characteristic , and let be a nonsingular projective curve over . We prove that for any real number $x \ge…
Milnor fibers and symplectic fillings of quotient surface singularities
Heesang Park, Jongil Park, Dongsoo Shin +1
We determine a one-to-one correspondence between Milnor fibers and minimal symplectic fillings of a quotient surface singularity (up to diffeomorphism type) by giving an explicit a…
Chern slopes of simply connected complex surfaces of general type are dense in [2,3]
Xavier Roulleau, Giancarlo Urzúa
We prove that for any number in , there are spin (resp. non-spin minimal) simply connected complex surfaces of general type with arbitrarily close…
Flipping surfaces
Paul Hacking, Jenia Tevelev, Giancarlo Urzúa
We study semistable extremal threefold neighborhoods following earlier work of Mori, Kollár, and Prokhorov. We classify possible flips and extend Mori's algorithm for computing fli…