All Questions

The well-known Max Noether's theorem for curves [see Arbarello-Cornalba-Griffiths-Harris Geometry of Algebraic Curves vol.1, p. 117] states that, if a smooth curve $C$ is non-hyperelliptic, then the ...

Let $\Lambda$ be a line arrangement in $\mathbb{P}^2$ and $n > 0$ an integer. Then Hirzebruch defined a smooth projective surface $H(\Lambda, n)$ as the minimal desingularization of a covering $Y \...

I'm seaching for a proof of the theorem below. Do you know any reference? Consider $f:X\rightarrow Y$ projective birational map between normal varieties and $\mathbb{R}$ cartier divisor $D$ whose ...

I learned some basic properties of Hirzebruch surface mainly from Vakil's notes "the rising sea", section 20.2.9. the Hirzebruch surface is defined as $\mathbb{F}_n:=\operatorname{Proj} (\...

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 ...

I am hoping to write down very explicitly the equations for the following data: an Enriques surface $X$ of type $\mathrm{Pic}^{\tau} = \mathbb{Z} / 2 \mathbb{Z}$ such that its canonical $\mu_2$-cover ...