# The generalized roof F(1,2,n): Hodge structures and derived categories

@inproceedings{Fatighenti2021TheGR, title={The generalized roof F(1,2,n): Hodge structures and derived categories}, author={Enrico Fatighenti and Michał Kapustka and Giovanni Mongardi and Marco Rampazzo}, year={2021} }

. We considergeneralizedhomogeneousroofs, i.e. quotientsof simplyconnected,semisimpleLie groupsbyaparabolic subgroup,whichadmittwo projectivebundlestructures. Givenageneralhyperplane section on such a variety, we study the zero loci of its pushforwards along the projective bundle structures and we discuss their properties at the level of Hodge structures. In the case of the ﬂag variety F (1 , 2 ,n ) with its projections to P n − 1 and G (2 ,n ) , we construct a derived embedding of the relevant…

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