Questions tagged [gaga]

Hi, Is there a simple example of an (affine) algebraic variety $X$ over $\mathbb C$ where the $H^*_{dR}(X/\mathbb C) = H^*(\Omega^\bullet_{A/\mathbb C})$ differs from the singular cohomology $H^*_{...

From a post to The Jouanolou trick: Are all topologically trivial (contractible) complex algebraic varieties necessarily affine? Are there examples of those not birationally equivalent to an affine ...

When is a Stein manifold a complex affine variety? I had thought that there was a theorem saying that a variety which is Stein and has finitely generated ring of regular functions implies affine, but ...

My question is as follows. Do the Chern classes as defined by Grothendieck for smooth projective varieties coincide with the Chern classes as defined with the aid of invariant polynomials and ...

Let $X/\mathbb{C}$ a nonsingular proper variety and $X_{an}$ it's associated analytic space. Is $X_{an}$ necessarily Kahler? Certainly we know this if $X$ is projective. A complex torus is algebraic ...

Let $M$ be a complex manifold admitting an atlas with each chart biholomorphic to $\mathbb{C}^n$ and transition maps being rational functions. Is it true that there exists a smooth integral ...