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32 votes
1 answer
1k views

About a claim by Gromov on proper holomorphic maps

At p. 223 of his paper [G03], Mikhail Gromov makes the following claim: Let $X$, $Y$ be two complex manifolds (not necessarily compact or Kähler) of the same dimension and having the same even Betti ...
Francesco Polizzi's user avatar
11 votes
1 answer
860 views

Is every surjective holomorphic self-map on a compact complex manifold finite-to-one?

I have already asked this question on stack exchange, but I didn’t get any answer. Let $X$ be a compact connected complex manifold. Let $f:X \to X$ be a surjective holomorphic map. Is it true that $f$...
Mayuresh L's user avatar
3 votes
1 answer
831 views

Are Lefschetz thimbles holomorphic manifolds?

I have a Lefschetz thimble defined by the stable flow of the gradient a holomorphic function toward a critical point (as defined e.g. in Witten arXiv:1001.2933 and F.Pham "Vanishing homologies and the ...
Luigi Scorzato's user avatar