Linear combinations of cohomological invariants of compact complex manifolds

Abstract: We will give answers to the following three questions about the set of all compact complex manifolds of a given dimension:

(i) Which linear relations between Hodge, Betti and Chern numbers are universally satisfied?

(ii) Which linear combinations of Hodge, Betti and Chern numbers are bimeromorphism invariants?

(iii) Which linear combinations of Hodge, Betti and Chern numbers are topological invariants?

We also present a strategy to answer the analogous questions when asked about `all' cohomological invariants (including e.g. the dimensions of higher pages of the Frölicher spectral sequence or Bott Chern and Aeppli cohomology). We carry this out to obtain answers in low dimensions, with answers in any dimension being reduced to specific construction problems.

Mathematics

Audience: researchers in the topic

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Geometry Seminar - University of Florence

Series comments: If you are interested in attending, please send a message to daniele.angella@unifi.it or francesco.pediconi@unifi.it.

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