All Questions

Given a general quartic surface $S$ in $\mathbf{P}^3$, there is a natural 6:1 surjective map $\phi: Hilb^2(S) \to G(1,3)$ sending $\{P,Q\}$ to the line through them in $\mathbf{P}^3$. Can you ...

The Hilbert scheme of 2 points on an elliptic curve $C$, $Hilb^2(C)$, has a natural structure of ruled surface, given by the map $f:Hilb^2(C) \to C$ such that $f(P,Q)=P+Q$. What can we say about the ...