All Questions

This is a simple question, just looking for a reference for a formula. As far I understand the genus of a prime Fano $n$-fold is defined to be the genus of a complete intersection of $n-1$ smooth ...

It is known that in general Globally Torelli does not imply the local Torelli theorem, see Is the Torelli map an immersion? Globally Torelli means that the period map $\mathcal{P}$ is injective and ...

A del Pezzo surface is a smooth, 2-dimensional projective variety $X$ with ample anticanonical divisor, i.e. a 2-dimensional Fano variety. I am interested in the arithmetic analogue, a 2-dimensional ...

The question is stated in the title, but I would like to add some motivation. I've been teaching a course on complex tori and abelian varieties this semester and I would like to end it by showing ...

Let $X$ be a projective Fano 3-fold or 4-fold and let $D^b(X)$ be the bounded derived category of coherent sheaves on $X$. For what $X$ is it known a semi orthogonal decomposition into indecomposable ...