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For questions about or involving complex manifolds.

2 votes
0 answers
198 views

Betti numbers of threefolds with trivial canonical class

I am interested in a simply-connected compact complex manifold $M$ of dimension three with trivial canonical class. Note that if it is K"ahler, then it is a Calabi-Yau threefold. Its independent Bett …
5 votes
1 answer
459 views

Threefolds with the same Betti numbers and the same Chern numbers

By a threefold, I mean a compact complex manifold of dimension three. My question is a simple one: Are there known INFINITELY many non-homeomorphic threefolds that have the same Betti numbers and the …
2 votes

Finite self-maps exist on rigid CY3s

One can show that such a map in the question doesn't exist (no need to assume simply-connectedness). As abx pointed out, any finite map between smooth projective varieties with trivial canonical bundl …
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