The 2-Dimensional Calabi Flow

M ar 2 00 6 On the Calabi flow

1 M ar 2 00 6 On the Calabi flow

Calabi flow and projective embeddings

Let X ⊂ CP be a smooth subvariety. We study a flow, called balancing flow, on the space of projectively equivalent embeddings of X which attempts to deform the given embedding into a balanced one. If L→ X is an ample line bundle, considering embeddings via H(L) gives a sequence of balancing flows. We prove that, provided these flows are started at appropriate points, they converge to Calabi flo...

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

S-duality and the Calabi-yau Interpretation of the N = 4 to N = 2 Flow

The action of the S-duality Sl(2, Z) group on the moduli of the Calabi-Yau manifold W IP 11226 appearing in the rank two dual pair (K 3 × T 2/W IP 11226) is defined by interpreting the N =4 to N =2 flow, for SU(2) supersymmetric YangMills, in terms of the Calabi-Yau moduli. The different singularity loci are mapped in a one to one way, and the (N =2 limit/point particle limit) is obtained in bo...