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Let $X\subset P^5$ be a smooth cubic fourfold. It is well known that its variety of lines $F(X)$ is a smooth fourfold Fano variety. Hence its derived category should have a semi-orthogonal ...

Let $X$ be a normal projective Fano variety, that is the anti-canonical divisor $-K_X$ is ample. For any $m>0$ let us consider the complete linear system $|-mK_X|$ and the map $$f_{|-mK_X|}:X\...

In the book of Iskovskikh and Prokhorov it seems not known wether the $V_1$, an hypersurface of degree $6$ in the weighted projective space $\mathbb{P}(3,2,1,1,1)$, is rational or not. Is there any ...