All Questions

(EDIT 07/06/11: although the question has not been settled definitely, Sándor's excellent answer and the comments by Angelo and ulrich have highlighted many potential obstructions to the constructions ...

I am aware from Borisov, Căldăraru, Perry and Ottem, Rennemo that what is known as the birational Torelli problem is false in general for Calabi-Yau threefolds, but I would like to know if there are ...

Take a finite field $\mathbb{F}_{\!q}$ such that $q \equiv 1 \pmod 3$, i.e., $\omega \mathrel{:=} \sqrt[3]{1} \in \mathbb{F}_{\!q}$, $\omega \neq 1$. Also, for $i \in \{0,1,2\}$ consider the elliptic ...

Let $(X,B)$ be a projective log canonical pair (here I mean $B \geq 0$). Assume that the coefficients of $B$ are rational, and that $K_X+B \equiv 0$. Is it true that $K_X + B \sim_\mathbb{Q} 0$? I ...

Let $X$ be a projective variety over $\mathbb{C}$, then the effective curves module the numerical equivalence form a cone. For my understanding, if the extreme ray $[C]$ has the property that $[C]\...

Let $X$ be a Calabi-Yau 3-fold with Picard number one. How can one show that the automorphism group $Aut(X)$ is finite and moreover coincides with the birational automorphism group $Bir(X)$? It seems ...