We consider 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 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 DOUBLE-STRUCK CAPITAL Pn- 1 and G(2,n), we construct a derived embedding of the relevant zero loci by methods based on the study of B-brane categories in the context of a gauged linear sigma model.
Fatighenti E., Kapustka M., Mongardi G., Rampazzo M. (2023). The Generalized Roof F(1, 2,n): Hodge Structures and Derived Categories. ALGEBRAS AND REPRESENTATION THEORY, 26(6), 2313-2342 [10.1007/s10468-022-10173-y].
The Generalized Roof F(1, 2,n): Hodge Structures and Derived Categories
Fatighenti E.
;Kapustka M.;Mongardi G.;Rampazzo M.
2023
Abstract
We consider 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 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 DOUBLE-STRUCK CAPITAL Pn- 1 and G(2,n), we construct a derived embedding of the relevant zero loci by methods based on the study of B-brane categories in the context of a gauged linear sigma model.| File | Dimensione | Formato | |
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