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arXiv · 2110.10475

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

Enrico Fatighenti·Michał Kapustka·Giovanni Mongardi·Marco Rampazzo
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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 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 $\mathbb{P}^{n-1}$ 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.

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Enrico Fatighenti, Michał Kapustka, Giovanni Mongardi, Marco Rampazzo. 2021-10-20. The generalized roof F(1,2,n): Hodge structures and derived categories. https://arxiv.org/abs/2110.10475

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