In Section 4, we shall give an easy counterexample using a rational elliptic surface with infinitely many (-1)-curves.
Let S be a rational elliptic surface with global sections whose Mordell-Weil rank is positive.
As shown in Figure 7, the local curve surface of the waist and the abdomen of the body is considered as an idea part of an elliptic surface
, which is noted as [[PI].sub.a].
A real elliptic surface will be a morphism [[PI].sub.1] : Y [right arrow] [P.sup.1] defined over R, when Y is a real algebraic surface such that over all but finitely many points in the basic curve, the fibre is a nonsingular curve of genus one.
After contracting all components of the fibres of [PI] that do not intersect the curve s([P.sup.1]), we obtain the Weierstrass model of the Jacobian elliptic surface [J.sup.w] with a proper map [??] : [J.sup.w] [right arrow] B where [J.sup.w] has at worst simple singular points, and a section s' : [P.sup.1] [right arrow] [J.sup.w] not passing through the singular points of [J.sup.w].
S'/X' is the nonsingular, relatively minimal elliptic surface
birational to the base change X' [x.sub.X] S of S/X by the projection f: X' [right arrow] X.
Top, An elliptic surface
related to sums of consecutive squares, Exposition.
* an elliptic surface
[pi]: [S.sub.[lambda]] [right arrow] [P.sup.1] (t-line) defined over [k.sub.0], and
Eleven contributions are selected from the eight working groups in the areas of elliptic surfaces
and the Mahler measure, analytic number theory, number theory in functions fields and algebraic geometry over finite fields, arithmetic algebraic geometry, K-theory and algebraic number theory, arithmetic geometry, modular forms, and arithmetic intersection theory.
QRT Maps and Elliptic Surfaces
, Springer Monographs in Mathematics, Springer, New York, NY, USA, 2010.
The aim of the experimental investigations was to correlate the predicted and real deviations of the curvature representation of elliptic surfaces
. The machining was carried out at the milling center Mikron VCE 500.
Degtyarev (Bilkent U., Ankara, Turkey) explores ramifications of the close relation between elliptic surfaces
and trigonal curves in ruled surfaces, skeletons (also called dessins d'enfants and quilts among other things), and subgroups of the modular group gamma : = PSL(2,Z).