# 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 classify generalized homogeneous roofs, i.e. quotients of simply connected, semisimple Lie groups by a parabolic subgroup, which admit two projective bundle structures. Given a general hyperplane section on such a variety, we consider 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 Pn−1 andG(2, n), we construct a derived embedding of…

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