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Type IIA on the conifold is a prototype example for engineering QED with onecharged hypermultiplet. The geometry admits a flop of length one. In thispaper, we study the next generation of geometric engineering on singulargeometries, namely flops of length two such as Laufer's example, which weaffectionately think of as the $\it{conifold\ 2.0}$. Type IIA on the lattergeometry gives QED with higher-charge states. In type IIB, even a singleD3-probe gives rise to a nonabelian quiver gauge theory. We study this class ofgeometries explicitly by leveraging their quiver description, showing how toparametrize the exceptional curve, how to see the flop transition, and how tofind the noncompact divisors intersecting the curve. With a view towardsF-theory applications, we show how these divisors contribute to the enhancementof the Mordell-Weil group of the local elliptic fibration defined by Laufer'sexample.

Geometric engineering on flops of length two