M ar 2 00 6 On the Calabi flow

1 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.

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

M ar 2 00 4 Computing the level of a modular rigid Calabi - Yau threefold Luis

In a previous article (cf. [DM]), the modularity of a large class of rigid Calabi-Yau threefolds was established. To make that result more explicit, we recall (and re-prove) a result of Serre giving a bound for the conductor of “integral” 2-dimensional compatible families of Galois representations and apply this result to give an algorithm that determines the level of a modular rigid Calabi-Yau...

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 .