Topological Formulae for the Zeroth Cohomology of Line Bundles on
Surfaces
Authors:
Callum R Brodie, Andrei Constantin, Rehan Deen, Andre Lukas
Abstract:
We identify a set of transforms on the Picard lattice of non-singular complex
projective surfaces that map effective line bundles to nef line bundles, while
preserving the dimension of the zeroth cohomology. These transforms can often
be used in conjunction with vanishing theorems to compute the dimension of the
zeroth cohomology in terms of a topological index. The method is illustrated on
del Pezzo and Hirzebruch surfaces.
