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We study threefolds $X \subset ℙ^{r}$ 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 embeddings...

On the reducibility of moduli spaces of stable 2-bundles over an elliptic surface.

Kai-Cheong Mong (1991)

Mathematische Zeitschrift

On the uniqueness of elliptic K3 surfaces with maximal singular fibre

Matthias Schütt, Andreas Schweizer (2013)

Annales de l’institut Fourier

We explicitly determine the elliptic $K 3$ surfaces with section and maximal singular fibre. If the characteristic of the ground field is different from $2$ , for each of the two possible maximal fibre types, $I_{19}$ and $I_{14}^{*}$ , the surface is unique. In characteristic $2$ the maximal fibre types are $I_{18}$ and $I_{13}^{*}$ , and there exist two (resp. one) one-parameter families of such surfaces.

Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface (II).

Indranil Biswas (2005)

Collectanea Mathematica

In [6], orbifold G-bundles on a certain class of elliptic fibrations over a smooth complex projective curve X were related to parabolic G-bundles over X. In this continuation of [6] we define and investigate holomorphic connections on an orbifold G-bundle over an elliptic fibration.

Persson's list of singular fibers for a rational elliptic surface.

Rick Miranda (1990)

Mathematische Zeitschrift

Rang de courbes elliptiques avec groupe de torsion non trivial

Odile Lecacheux (2003)

Journal de théorie des nombres de Bordeaux

On construit des courbes elliptiques sur $ℚ (T)$ de rang au moins 3, avec un sous-groupe de torsion non trivial. Par spécialisation, des courbes elliptiques de rang 5 et 6 sur $ℚ$ sont obtenues.