Let $Y$ be Gushel-Mukai threefold and $X$ a Gushel-Mukai fourfold containing $Y$ as its hyperplane section, the semi-orthogonal decomposition of $X$ and $Y$ are both known. Also, for cubic fourfold and its hyperplane section, a cubic threefold, the semi-orthogonal decomposition are both known. What about others? For example, are there any Fano fourfold $Z$ containing degree 14, 16, 18 index one prime Fano threefold such that semiorthogonal decomposition of $Z$ is known?
$\begingroup$
$\endgroup$
4
-
2$\begingroup$ Yes, all these fourfolds have SODs provided by homological projective duality for $Gr(2,6)$, $LGr(3,6)$ and $G_2Gr(2,7)$, respectively. $\endgroup$– SashaCommented Dec 31, 2021 at 7:28
-
$\begingroup$ Thanks Sasha, is there any reference for these? $\endgroup$– user41650Commented Dec 31, 2021 at 7:35
-
2$\begingroup$ The last two cases are discussed here: Kuznetsov, A. G. Hyperplane sections and derived categories. (Russian) ; translated from Izv. Ross. Akad. Nauk Ser. Mat. 70 (2006), no. 3, 23--128 Izv. Math. 70 (2006), no. 3, 447--547, and the first case here: arxiv.org/abs/math/0610957. $\endgroup$– SashaCommented Dec 31, 2021 at 7:40
-
$\begingroup$ Thanks so much Sasha, happy new year! $\endgroup$– user41650Commented Dec 31, 2021 at 7:41
Add a comment
|