• Corpus ID: 239049671

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

@inproceedings{Fatighenti2021TheGR,
  title={The generalized roof F(1,2,n): Hodge structures and derived categories},
  author={Enrico Fatighenti and Michał Kapustka and Giovanni Mongardi and Marco Rampazzo},
  year={2021}
}
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 Pn−1 andG(2, n), we construct a derived embedding of… 

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SHOWING 1-10 OF 42 REFERENCES
Quotients of affine spaces for actions of reductive groups
In this paper we study actions of reductive groups on affine spaces. We prove that there is a fan structure on the space of characters of the group, which parameterizes the possible invariant
Nested varieties of K3 type
Using geometrical correspondences induced by projections and two-steps flag varieties, and a generalization of Orlov's projective bundle theorem, we relate the Hodge structures and derived categories
Mukai duality and roofs of projective bundles
We investigate a construction providing pairs of Calabi-Yau varieties described as zero loci of pushforwards of a hyperplane section on a roof as described by Kanemitsu. We discuss the implications
Phases Of N=2 Theories In 1+1 Dimensions With Boundary
We study B-type D-branes in linear sigma models with Abelian gauge groups. The most important finding is the grade restriction rule. It classifies representations of the gauge group on the Chan-Paton
Variation of geometric invariant theory quotients and derived categories
We study the relationship between derived categories of factorizations on gauged Landau–Ginzburg models related by variations of the linearization in Geometric Invariant Theory. Under assumptions
Equivalences Between GIT Quotients of Landau-Ginzburg B-Models
We define the category of B-branes in a (not necessarily affine) Landau-Ginzburg B-model, incorporating the notion of R-charge. Our definition is a direct generalization of the category of perfect
The Penrose Transform: Its Interaction with Representation Theory
Part 1 Lie algebras and flag manifolds: some structure theory borel and parabolic subalgebras generalized flag varieties fibrations of generalized flag varieties. Part 2 Homogeneous vector bundles on
A geometric approach to Orlov’s theorem
Abstract A famous theorem of D. Orlov describes the derived bounded category of coherent sheaves on projective hypersurfaces in terms of an algebraic construction called graded matrix factorizations.
Divisors in the moduli space of Debarre-Voisin varieties
Let V10 be a 10-dimensional complex vector space and let σ ∈ ∧ V ∨ 10 be a non-zero alternating 3-form. One can define several associated degeneracy loci: the Debarre– Voisin variety X 6 ⊂ Gr(6,
A survey on the Campana-Peternell Conjecture
In 1991 Campana and Peternell proposed, as a natural algebro-geometric extension of Mori's characterization of the projective space, the problem of classifying the complex projective Fano manifolds
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