Elliptic Calabi-Yau threefolds over a del Pezzo surface

Abstract

We consider certain elliptic threefolds over the projective plane (more generally over certain rational surfaces) with a section in Weierstrass normal form. In particular, over a del Pezzo surface of degree 8, these elliptic threefolds are Calabi-Yau threefolds. We will discuss especially the generating functions of Gromov-Witten and Gopakumar-Vafa invariants.

14 pages

References in corpus (2)

• A conjectural generating function for numbers of curves on surfaces
• Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces