Vanishing theorems for higher cohomology groups of the structural sheaf on certain complex topological vector spaces

摘要

Let (E,|| ||) be a complex normed space, E' its dual and B_1 C E' the dual of the unit ball of E. Equip E' and hence B1 with the weak*-topology s(E,E'), but call E'k the space E' with the kelleyfication topology of s(E, E') and use the corresponding complex structure. Here we prove that for every q≥2 and for every i≥1. Let M be a complex manifold locally modelled over an infinite-dimensional Banach space with countable unconditional basis and with the localizing property. Let S C M be a discrete subset and E a locally free sheaf on M with finite rank. Here we prove that the natural map is bijective.