The generalized roof F(1,2,n): Hodge structures and derived categories
Abstract
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 $\mathbb{P}^{n1}$ 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.10475
 Bibcode:
 2021arXiv211010475F
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory;
 14J45;
 14J81;
 14F08;
 14C30;
 14M15
 EPrint:
 26 pages, comments welcome!