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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.

2 votes
1 answer
110 views

Intersection of superlevel set of polynomials

Let $P_1$ and $P_2$ be complex polynomials with complex coefficients and $c > 0$. Can we find polynomial $P_3$ and $c’>0$ such that $\{z \in \mathbb C : |P_1(z)| \geq c\} \cap \{ z \in \mathbb C : …
Mayuresh L's user avatar
6 votes

Embedding open connected Riemann surfaces in $\mathbb{C}^2$

One of the first example of proper embedding of open Riemann surface is, Proper embedding of open unit disk in $\mathbb C^2$ which is one of corollary of Fatou-Bieberbach domains (holomorphic dynamic …
Mayuresh L's user avatar
11 votes
1 answer
846 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