On the extendability of elliptic surfaces of rank two and higher

Angelo Felice Lopez; Roberto Muñoz; José Carlos Sierra

Displaying similar documents to “On the extendability of elliptic surfaces of rank two and higher”

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.

Very ampleness of multiples of principal polarization on degenerate Abelian surfaces.

Alessandro Arsie (2005)

Revista Matemática Complutense

Similarity:

Quite recently, Alexeev and Nakamura proved that if Y is a stable semi-Abelic variety (SSAV) of dimension g equipped with the ample line bundle O(1), which deforms to a principally polarized Abelian variety, then O(n) is very ample as soon as n ≥ 2g + 1, that is n ≥ 5 in the case of surfaces. Here it is proved, via elementary methods of projective geometry, that in the case of surfaces this bound can be improved to n ≥ 3.

Semipolarized nonruled surfaces with sectional genus two.

Biancofiore, Aldo, Fania, Maria Lucia, Lanteri, Antonio (2006)

Beiträge zur Algebra und Geometrie

Similarity:

A 4₃ configuration of lines and conics in ℙ⁵

Tomasz Szemberg (1994)

Annales Polonici Mathematici

Similarity:

Studying the connection between the title configuration and Kummer surfaces we write explicit quadratic equations for the latter. The main results are presented in Theorems 8 and 16.

A note on k-very ampleness of a bundle on a blown up plane.

Tutaj-Gasińska, Halszka (2003)

Beiträge zur Algebra und Geometrie

Similarity:

Obstructions to deforming curves on a $3$ -fold, II: Deformations of degenerate curves on a del Pezzo $3$ -fold

Hirokazu Nasu (2010)

Annales de l’institut Fourier

Similarity:

We study the Hilbert scheme ${Hilb}^{s c} V$ of smooth connected curves on a smooth del Pezzo $3$ -fold $V$ . We prove that any degenerate curve $C$ , any curve $C$ contained in a smooth hyperplane section $S$ of $V$ , does not deform to a non-degenerate curve if the following two conditions are satisfied: (i) $χ (V, ℐ_{C} (S)) \geq 1$ and (ii) for every line $ℓ$ on $S$ such that $ℓ \cap C = \emptyset$ , the normal bundle $N_{ℓ / V}$ is trivial ( $N_{ℓ / V} ≃ {𝒪_{ℙ^{1}}}^{\oplus 2}$ ). As a consequence, we prove an analogue (for ${Hilb}^{s c} V$ ) of a conjecture of J. O. Kleppe, which is concerned with non-reduced components...

Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces

Klaus Hulek, Remke Kloosterman (2011)

Annales de l’institut Fourier

Similarity:

In this paper we give a method for calculating the rank of a general elliptic curve over the field of rational functions in two variables. We reduce this problem to calculating the cohomology of a singular hypersurface in a weighted projective $4$ -space. We then give a method for calculating the cohomology of a certain class of singular hypersurfaces, extending work of Dimca for the isolated singularity case.

The Frobenius action on rank $2$ vector bundles over curves in small genus and small characteristic

Laurent Ducrohet (2009)

Annales de l’institut Fourier

Similarity:

Let $X$ be a general proper and smooth curve of genus $2$ (resp. of genus $3$ ) defined over an algebraically closed field of characteristic $p$ . When $3 \leq p \leq 7$ , the action of Frobenius on rank $2$ semi-stable vector bundles with trivial determinant is completely determined by its restrictions to the 30 lines (resp. the 126 Kummer surfaces) that are invariant under the action of some order $2$ line bundle over $X$ . Those lines (resp. those Kummer surfaces) are closely related to the elliptic curves (resp....