Displaying similar documents to “A family of varieties with exactly one pointless rational fiber”

Projective quartics revisited

T. Szemberg, H. Tutaj-Gasińska (1999)

Annales Polonici Mathematici

Similarity:

We classify all smooth projective varieties of degree 4 and describe their syzygies.

The geometry of the third moment of exponential sums

Florent Jouve (2008)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We give a geometric interpretation (and we deduce an explicit formula) for two types of exponential sums, one of which is the third moment of Kloosterman sums over F q of type K ( ν 2 ; q ) . We establish a connection between the sums considered and the number of F q -rational points on explicit smooth projective surfaces, one of which is a K 3 surface, whereas the other is a smooth cubic surface. As a consequence, we obtain, applying Grothendieck-Lefschetz theory, a generalized formula for the third moment...

Density of rational points on cyclic covers of ℙ n

Ritabrata Munshi (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We obtain upper bound for the density of rational points on the cyclic covers of ℙ n . As n → ∞ our estimate tends to the conjectural bound of Serre.

On the extendability of elliptic surfaces of rank two and higher

Angelo Felice Lopez, Roberto Muñoz, José Carlos Sierra (2009)

Annales de l’institut Fourier

Similarity:

We study threefolds X ⊂ ℙ r having as hyperplane section a smooth surface with an elliptic fibration. We first give a general theorem about the possible embeddings of such surfaces with Picard number two. More precise results are then proved for Weierstrass fibrations, both of rank two and higher. In particular we prove that a Weierstrass fibration of rank two that is not a K3 surface is not hyperplane section of a locally complete intersection threefold and we give some conditions, for many...

Siegel’s theorem and the Shafarevich conjecture

Aaron Levin (2012)

Journal de Théorie des Nombres de Bordeaux

Similarity:

It is known that in the case of hyperelliptic curves the Shafarevich conjecture can be made effective, i.e., for any number field k and any finite set of places S of k , one can effectively compute the set of isomorphism classes of hyperelliptic curves over k with good reduction outside S . We show here that an extension of this result to an effective Shafarevich conjecture for of hyperelliptic curves of genus g would imply an effective version of Siegel’s theorem for integral points...

Boundedness for threefolds in P containing a smooth ruled surface as hyperplane section.

Pietro Sabatino (2005)

Revista Matemática Complutense

Similarity:

Let X ⊂ P be a smooth irreducible projective threefold, and d its degree. In this paper we prove that there exists a constant β such that for all X containing a smooth ruled surface as hyperplane section and not contained in a fourfold of degree less than or equal to 15, d ≤ β. Under some more restrictive hypothesis we prove an analogous result for threefolds containing a smooth ruled surface as hyperplane section and contained in a fourfold of degree less than or equal to 15. ...