The Generalized Roof F(1, 2,n): Hodge Structures and Derived Categories

• Published in: Algebras and representation theory Vol. 26; no. 6; pp. 2313 - 2342
• Main Authors: Fatighenti, Enrico, Kapustka, Michał, Mongardi, Giovanni, Rampazzo, Marco
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.12.2023; Springer Nature B.V
• Subjects: Associative Rings and Algebras; Commutative Rings and Algebras; Hyperplanes; Lie groups; Mathematics; Mathematics and Statistics; Non-associative Rings and Algebras; Subgroups; 14J81 relationship with physics; 14C30 transcendental methods, Hodge theory (algebro-geometric aspects); 14M15 Grassmannians, Schubert varieties, flag manifolds; 14F08 derived categories of sheaves, dg categories, and related constructions in algebraic geometry; 14J45 Fano varieties; F08
• ISSN: 1386-923X; 1572-9079
• DOI: 10.1007/s10468-022-10173-y

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 ℙ n − 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.