arXiv subjects
Publications and source records attributed to Giosuè Emanuele Muratore.
Beauville and Donagi proved that the variety of lines $F(Y)$ of a smooth cubic fourfold $Y$ is a hyperkähler variety. Recently, C. Lehn, M.Lehn, Sorger and van Straten proved that one can naturally associate a hyperKähler variety $Z(Y)$ to the variety of twisted cubics on $Y$. Then, Voisin defined a degree 6 rational map $ψ:F(Y)\times F(Y)\dashrightarrow Z(Y)$. We will show that the indeterminacy locus of $ψ$ is the locus of intersecting lines.
The 2-Fano varieties, defined by De Jong and Starr, satisfy some higher dimensional analogous properties of Fano varieties. We propose a definition of (weak) $k$-Fano variety and conjecture the polyhedrality of the cone of pseudoeffective $k$-cycles for those varieties in analogy with the case $k=1$. Then, we calculate some Betti numbers of a large class of $k$-Fano varieties to prove some special case of the conjecture. In particular, the conjecture is true for all 2-Fano varieties of index $\ge n-2$, and also we complete the classification of weak 2-Fano varieties of Araujo and Castravet.