The Generalized Roof F(1, 2,n): Hodge Structures and Derived Categories
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 str...
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Published in | Algebras and representation theory Vol. 26; no. 6; pp. 2313 - 2342 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Dordrecht
Springer Netherlands
01.12.2023
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 1386-923X 1572-9079 |
DOI: | 10.1007/s10468-022-10173-y |