Carlos Rito

collaborators

5 papers

math.AG2026

Quintic surfaces with 18 cusps

Lev Borisov, Carlos Rito

We construct quintic surfaces in the three-dimensional projective space $P^{3}$ with $18$ ordinary cusps. Our starting point is the Barth--Rams description of quintics contai…

math.AG2026

Explicit Bicanonical Models of Eight Fake Quadrics

Lev Borisov, Carlos Rito

We compute explicit defining equations for eight fake quadrics arising as $Z /2 \times Z /4$ -covers of two singular $Z /2$ -Godeaux surfaces obtained in earlier w…

math.AG2026

Computation of Singular Godeaux Surfaces and a New Explicit Fake Quadric (With an Appendix by Christian Gleissner and Noah Ruhland)

Carlos Rito, Christian Gleissner, Noah Ruhland

We present a computational method for detecting highly singular members in families of algebraic varieties. Applying this approach to a family of numerical Godeaux surfaces, we obt…

math.AG2026

$Z /2$ -Godeaux surfaces

Eduardo Dias, Carlos Rito

We prove that the moduli space of numerical Godeaux surfaces with torsion group $Z /2$ is irreducible and unirational of dimension 8. Moreover, we show that the topological…

math.AG2025

On a sequence of singular ball quotient surfaces on the line $K^{2} = 9 I ¨ - 18$

Carlos Rito, Xavier Roulleau

Starting from computer experiments with the fundamental group of the Cartwright--Steger surface, we construct an infinite tower $(X_{n})_{n \geq 1}$ of normal projective surfaces obtai…

Quintic surfaces with 18 cusps

Explicit Bicanonical Models of Eight Fake Quadrics

Computation of Singular Godeaux Surfaces and a New Explicit Fake Quadric (With an Appendix by Christian Gleissner and Noah Ruhland)

Z/2-Godeaux surfaces

On a sequence of singular ball quotient surfaces on the line K2=9I¨−18

$Z /2$ -Godeaux surfaces

On a sequence of singular ball quotient surfaces on the line $K^{2} = 9 I ¨ - 18$