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## The construction problem for Hodge numbers

### Matthias Paulsen (LMU München)

#### Freitag, 25. Oktober 2019 10:30Uhr

To a smooth complex projective variety, one often associates its Hodge diamond, which consists of all Hodge numbers and thus collects important numerical invariants. One might ask which Hodge diamonds are possible in a given dimension.

A complete classification of the possible Hodge diamond seems to be out of reach, since unexpected inequalities between the Hodge numbers occur in some cases. However, I will explain in this talk that the above construction problem is completely solvable if we consider the Hodge numbers modulo an arbitrary integer. One consequence of this result is that every polynomial relation between the Hodge numbers in a given dimension is induced by the Hodge symmetries. This is joint work with Stefan Schreieder.