All Questions

Suppose I have a closed subvariety $V$ of $\mathbb P^n \times \mathbb A^m$ given by explicit equations. Is it possible in practice to compute the coherent cohomology of $V$ with coefficients in a line ...

I have a quasiprojective variety given by some explicit quations. How do I compute its coherent cohomology (with coefficients in the structure sheaf)? Do I use the Cech complex for an open affine ...

Let $\pi:X\to Y$ be a proper map of algebraic varieties (over $\mathbb C$) which is a bi-rational equivalence. are the following statements equivalent? The derived direct image of $O_X$ is $O_Y$. ...