All Questions

I have a question about vector bundles on the algebraic surface $\mathbb{P}^1\times\mathbb{P}^1$. My motivation is the splitting theorem of Grothendieck, which says that every algebraic vector bundle ...

What do people mean by the "cyclic cover trick"? I have found this expression a couple of times with no complete explanation, both talking about curves and surfaces...

These are some questions concerning Mumford's "Lectures on curves on an algebraic surface". We concern ourselves with questions of the Picard variety $P$, and its dimension, of a complete nonsingular ...

Consider a finite field $\mathbb{F}_p$ (where $p \equiv 1 \ (\mathrm{mod} \ 3)$, $p \equiv 3 \ (\mathrm{mod} \ 4)$) and the elliptic curve $$ E\!:y^2 = x^3 + (t^6 + 1)^2 $$ over the univariate ...