All Questions

In the article "The irreducibility of the space of curves of given genus" by Deligne, Mumford, the definition of stable curves start with the assumption that the genus is at least $2$. Why is this ...

Let $f:X \to Y$ be a proper, birational morphism with connected fibers, $X$ is non-singular and $Y$ is normal. Does there exist a moduli space parametrizing all invertible sheaves $\mathcal{L}$ on $X$ ...