Related papers: Degree two unirational parametrizations over the r…
We give a complete characterization of degree two rational maps with potential good reduction over local fields. We show this happens exactly when the map corresponds to an integral point in the moduli space. We detail an algorithm by which…
We classify surfaces of general type whose bicanonical map is composed with a rational map of degree 2 onto a rational or ruled surface.
Given a unirational parameterization of a surface, we present a general algorithm to determine a birational parameterization without using parameterization algorithms. Additionally, if the surface is assumed to have a birational…
We present an algorithm for computing curves and families of curves of prescribed degree and geometric genus on real rational surfaces.
A K3 surface over a number field has infinitely many rational points over a finite field extension. For K3 surfaces of degree 2, arising as double covers of $\mathbb{P}^2$ branched along a smooth sextic curve, we give a bound for the degree…
We study arithmetic degree of a dominant rational self-map on a smooth projective variety over a function field of characteristic zero. We see that the notion of arithmetic degree and some related problems over function fields are…
We study and classify linearly normal surfaces in $\mathbf{P}^n$, of degree $d$ and sectional genus $g$, such that $d\geq 2g-1$.
We classify the automorphism groups of del Pezzo surfaces of degrees one and two over an algebraically closed field of characteristic two. This finishes the classification of automorphism groups of del Pezzo surfaces in all characteristics.
We study equivariant birational geometry of (rational) quartic double solids ramified over (singular) Kummer surfaces.
We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.
Hirschfeld classified split del Pezzo surfaces of degree at least three whose points are all contained on the lines in the surface. We continue his work and begin the classification of split degree two del Pezzo surfaces over finite fields…
We give an upper bound for the degree of rational curves in a family that covers a given birational ruled surface in projective space. The upper bound is stated in terms of the degree, sectional genus and arithmetic genus of the surface. We…
This paper shows that the multiplicity of the base points locus of a projective rational surface parametrization can be expressed as the degree of the content of a univariate resultant. As a consequence, we get a new proof of the degree…
We describe smooth rational projective algebraic surfaces over an algebraically closed field of characteristic different from 2 which contain $n \ge \b_2-2$ disjoint smooth rational curves with self-intersection -2, where $\b_2$ is the…
We introduce the notion of radical parametrization of a surface, and we provide algorithms to compute such type of parametrizations for families of surfaces, like: Fermat surfaces, surfaces with a high multiplicity (at least the degree…
We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools from analytic number theory.
A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit…
We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address the cases of non-ordinary and non-simple varieties. For each…
We study the birational properties of geometrically rational surfaces from a derived categorical point of view. In particular, we give a criterion for the rationality of a del Pezzo surface over an arbitrary field, namely, that its derived…
We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.