[email protected] ELLIPTIC CURVE CONFIGURATIONS ON FANO SURFACES
نویسنده
چکیده
We give the classification of the configurations of the elliptic curves on the Fano surface of a smooth cubic threefold. That means that we give the number of such curves, their intersections and a plane model. This classification is linked to the classification of the automorphism groups of theses surfaces. The Fano surface of the Fermat cubic of P is the only one to contain 30 elliptic curves and we study its properties in detail. MSC: 14J29 (primary); 14J45, 14J50, 14J70, 32G20 (secondary). Key-words: Surfaces of general type, Ample cotangent sheaf, Cotangent map, Fano surface of a cubic threefold, Configurations of elliptic curves, Automorphisms, Maximal Picard number, Fano varieties, Intermediate Jacobians.
منابع مشابه
The Fano Surface of the Klein Cubic Threefold
We prove that the Klein cubic threefold F is the only one cubic threefold which has an order 11 automorphism. We calculate the period lattice of the intermediate Jacobian of F and study its Fano surface S. We compute the set of fibrations of S on a curve of positive genus and the intersection between the fibres of these fibrations. These fibres generate an index 2 sub-group of the Néron-Severi ...
متن کاملVector Bundles on a K3 Surface
A K3 surface is a quaternionic analogue of an elliptic curve from a view point of moduli of vector bundles. We can prove the algebraicity of certain Hodge cycles and a rigidity of curve of genus eleven and gives two kind of descriptions of Fano threefolds as applications. In the final section we discuss a simplified construction of moduli spaces. 2000 Mathematics Subject Classification: 14J10, ...
متن کاملON THE HYPERBOLICITY OF SURFACES OF GENERAL TYPE WITH SMALL c1
Surfaces of general type with positive second Segre number s2 := c1 − c2 > 0 are known by results of Bogomolov to be algebraically quasihyperbolic i.e. with finitely many rational and elliptic curves. These results were extended by McQuillan in his proof of the Green-Griffiths conjecture for entire curves on such surfaces. In this work, we study hyperbolic properties of minimal surfaces of gene...
متن کاملar X iv : 0 90 1 . 32 11 v 1 [ m at h . A G ] 2 1 Ja n 20 09 COMPACT KÄHLER MANIFOLDS WITH ELLIPTIC HOMOTOPY TYPE
Simply connected compact Kähler manifolds of dimension up to three with elliptic homotopy type are characterized in terms of their Hodge diamonds. This is applied to classify the simply connected Kähler surfaces and Fano threefolds with elliptic homotopy type.
متن کاملEfficient elliptic curve cryptosystems
Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...
متن کامل