All Questions

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 \...

Let $f\in \mathbb{C}[x,y]$ be an irreducible polynomial. Let $n>0$ be an integer such that the hypersurface $S:=\{ (x,y,z)\in \mathbb{C}^3|z^n=f(x,y) \}$ is a connected complex submanifold of $\...

Does there exist a smooth projective complex surface $X$ such that, (1) $\pi_1(X) = 0$ (2) $\Omega_X^1$ is ample (3) the Mumford-Tate group of $H^2(X)$ is a torus There exist examples with any two of ...