14 dec 2016 -- 15:00
Aula di Consiglio, Dip.Matematica, Università "La Sapienza", Roma
Abstract.
Let M be an n-dimensional complex manifold and f,g two distinct holomorphic self-maps of M. Suppose that f and g coincide on a globally irreducible compact hypersurface S of M. If one of the two maps is a local biholomorphism in a neighborhood of the regular part S' of S and, if needed, S' sits into M in a particular nice way, then it is possible to define a 1-dimensional holomorphic (possibly singular) foliation on S' and a partial holomorphic connection on the normal bundle of S' in M.
As a consequence, one can localize the (n-1)-th power of the first Chern class of the line bundle $[S]$ on M canonically induced by S and thus get an index theorem.