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 …

There's already a question (which got several interesting answers) asking about examples of the phenomenon of non (essential) injectivity of the functor $U:Alg\to AnEsp$, mapping e …

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 …

I am trying to understand the idea behind the proof of GAGA. A crucial step is the following: Theorem: Let $X=\mathbb{P}^r_{\mathbb{C}}$ (either as a variety or as an analytic spa …

Let $X$ be a nice variety over $\mathbb{C}$, where nice probably means smooth and proper. I want to know: How can we show that the hypercohomology of the algebraic de Rham complex …

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 pol …

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

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 …