F-Theory Compactifications with Multiple U(1)-Factors: Constructing Elliptic Fibrations with Rational Sections

Understand

We study F-theory compactifications with U(1)xU(1) gauge symmetry on elliptically fibered Calabi-Yau manifolds with a rank two Mordell-Weil group.

• We find that the natural presentation of an elliptic curve E with two rational points and a zero point is the generic Calabi-Yau onefold in dP_2.
• We determine the birational map to its Tate and Weierstrass form and the coordinates of the two rational points in Weierstrass form.
• We discuss its resolved elliptic fibrations over a general base B and classify them in the case of B=P^2.