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Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.

4 votes
0 answers
290 views

Is there an Ax-Grothendieck result for entire functions?

The Ax-Grothendieck result states that any polynomial injective function from $\mathbb{C}^n$ to itself is surjective. Is there such a statement for entire functions ?
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5 votes
0 answers
278 views

Smooth quotients and separation of orbits

Consider a unipotent algebraic group $G$ over $\mathbb{C}$ acting polynomially on $\mathbb{C}^n$. Suppose that the quotient exists as an analytical geometric quotient, i.e., $\mathbb{C}^n/G$ is a smo …
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