# Residual categories for (co)adjoint Grassmannians in classical types

@article{Kuznetsov2021ResidualCF, title={Residual categories for (co)adjoint Grassmannians in classical types}, author={Alexander Kuznetsov and Maxim Smirnov}, journal={Compositio Mathematica}, year={2021}, volume={157}, pages={1172 - 1206} }

In our previous paper we suggested a conjecture relating the structure of the small quantum cohomology ring of a smooth Fano variety of Picard number 1 to the structure of its derived category of coherent sheaves. Here we generalize this conjecture, make it more precise, and support it by the examples of (co)adjoint homogeneous varieties of simple algebraic groups of Dynkin types $\mathrm {A}_n$ and $\mathrm {D}_n$, that is, flag varieties $\operatorname {Fl}(1,n;n+1)$ and isotropic orthogonal…

## 12 Citations

On the derived category of the adjoint Grassmannian of type F

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- 2021

We construct a full rectangular Lefschetz collection in the derived category of the adjoint Grassmannian in type F4. This gives the first example of a full exceptional collection on this variety and…

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. This paper is devoted to the study of the quantum cohomology of coadjoint varieties of simple algebraic groups across all Dynkin types. We determine the non-semisimple factors of the small quantum…

The structure of exceptional sequences on toric varieties of Picard rank two

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For a smooth projective toric variety of Picard rank two we classify all exceptional sequences of invertible sheaves which have maximal length. In particular, we prove that unlike non-maximal…

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We discuss recent developments in the study of semiorthogonal decompositions of algebraic varieties with an emphasis on their behaviour in families. First, we overview new results concerning…

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We describe in terms of spherical twists the Serre functors of many interesting semiorthogonal components, called residual categories, of the derived categories of projective varieties. In…

A G ] 1 6 Ju l 2 02 1 ON THE DERIVED CATEGORY OF THE ADJOINT GRASSMANNIAN OF TYPE

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- 2021

We construct a full rectangular Lefschetz collection in the derived category of the adjoint Grassmannian in type F4. This gives the first example of a full exceptional collection on this variety and…

Cyclic group actions on Fukaya categories and mirror symmetry

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- 2020

Let $(X,\omega)$ be a compact symplectic manifold whose first Chern class $c_1(X)$ is divisible by a positive integer $n$. We construct a $\mathbb{Z}_{2n}$-action on its Fukaya category $Fuk(X)$ and…

Graph potentials and moduli spaces of rank two bundles on a curve

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We introduce graph potentials, which are Laurent polynomials associated to (colored) trivalent graphs. These graphs encode degenerations of curves to rational curves, and graph potentials encode…

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. We propose a conjectural semiorthogonal decomposition for the derived category of the moduli space of stable rank 2 bundles with xed determinant of odd degree, independently formulated by…

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