All Questions

Let $V\subset\mathbb{P}^5$ be the Veronese surface and let $X\subset\mathbb{P}^6$ be the cone over it. Since $X$ is $\mathbb{Q}$-factorial there are two integers $a,b$ such that $aK_X = \mathcal{O}_X(...

Let $\phi:X\dashrightarrow Y$ be a generically finite, dominant rational map between smooth projective varieties over $\mathbb{C}$. Assume that $Y$ is of general type. May we conclude then that $X$ ...

Can anyone help me with the following question? Let $X$ be a smooth, projective algebraic variety over a field $k$ of characteristic zero. Let $D$ be an effective divisor on $X$ and $m \geq 2$ an ...