1 M ar 2 00 6 On the Calabi flow

M ar 2 00 6 On the Calabi flow

6 M ar 2 00 9 A modular quintic Calabi - Yau threefold of level 55 Edward

In this note we search the parameter space of Horrocks-Mumford quintic threefolds and locate a Calabi-Yau threefold which is modular, in the sense that the L-function of its middle-dimensional cohomology is associated to a classical modular form of weight 4 and level 55.

ar X iv : 0 70 4 . 35 30 v 2 [ m at h . D G ] 2 5 O ct 2 00 7 Invariant forms , associated bundles and Calabi - Yau metrics

We develop a method, initially due to Salamon, to compute the space of " invariant " forms on an associated bundle X = P ×G V , with a suitable notion of invariance. We determine sufficient conditions for this space to be d-closed. We apply our method to the construction of Calabi-Yau metrics on T CP 1 and T CP 2 .

. D G ] 2 6 O ct 2 00 7 On the Calabi flow

ar X iv : h ep - t h / 04 07 25 2 v 1 2 9 Ju l 2 00 4 Flux Vacua Statistics for Two - Parameter Calabi - Yau ’ s

We study the number of flux vacua for type IIB string theory on an orientifold of the Calabi-Yau expressed as a hypersurface in WCP 4 [1, 1, 2, 2, 6] by evaluating a suitable integral over the complex-structure moduli space as per the conjecture of Douglas and Ashok. We show that away from the singular conifold locus, one gets the expected power law, and that the (neighborhood) of the conifold ...