Derived category automorphisms from mirror symmetry

Horja, R. Paul

doi:10.1215/s0012-7094-04-12711-3

Cited by 73 publications

(84 citation statements)

References 36 publications

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“…We will make extensive use of this technology in the rest of the paper. Our notation follows [23]. Given two non-singular proper algebraic varieties, X 1 and…”

Section: Fourier-mukai Functorsmentioning

confidence: 99%

“…, i * M (−1) , i * M (0) is the C 2 /Z n quiver. To evaluate the Ext-groups we use the stacky version of the spectral sequence (120), as presented for example in [49], and adapted to our case i : 23 For E and F two objects in the bounded derived category of the stack Y = P 1 (k, n − k) the spectral sequence reads…”

Section: The C 2 /Z N Quiver From Partial Resolutionsmentioning

confidence: 99%

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$$\mathbb{C}^2/\mathbb{Z}_{n}$$ Fractional Branes and Monodromy

Karp¹

2006

Commun. Math. Phys.

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We construct geometric representatives for the C 2 /Z n fractional branes in terms of branes wrapping certain exceptional cycles of the resolution. In the process we use large radius and conifold-type monodromies, and also check some of the orbifold quantum symmetries. We find the explicit Seiberg-duality which connects our fractional branes to the ones given by the McKay correspondence. We also comment on the Harvey-Moore BPS algebras.

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“…We will make extensive use of this technology in the rest of the paper. Our notation follows [23]. Given two non-singular proper algebraic varieties, X 1 and…”

Section: Fourier-mukai Functorsmentioning

confidence: 99%

Section: The C 2 /Z N Quiver From Partial Resolutionsmentioning

confidence: 99%

$$\mathbb{C}^2/\mathbb{Z}_{n}$$ Fractional Branes and Monodromy

Karp¹

2006

Commun. Math. Phys.

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“…Our notation follows. 24 Given two nonsingular proper algebraic varieties, X 1 and X 2 , an object K D͑X 1 ϫ X 2 ͒ determines a functor of triangulated categories ⌽ K :D͑X 1 ͒ → D͑X 2 ͒ by the formula 6…”

Section: A Fourier-mukai Functorsmentioning

confidence: 99%

On the Cn/Zm fractional branes

Karp¹

2009

Journal of Mathematical Physics

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We construct several geometric representatives for the C n / Z m fractional branes on either a partially or the completely resolved orbifold. In the process we use large radius and conifold-type monodromies and provide a strong consistency check. In particular, for C 3 / Z 5 we give three different sets of geometric representatives. We also find the explicit Seiberg duality which connects our fractional branes to the ones given by the McKay correspondence.

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“…this is just the kernel of [9, (4.31)], proved to be invertible in [10]. The point is that this definition makes sense whether or not there is a contraction morphism on X contracting D j alone.…”

Section: 2mentioning

confidence: 99%

Artin group actions on derived categories of threefolds

Szendrői¹

2004

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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Motivated by the enhanced gauge symmetry phenomenon of the physics literature and mirror symmetry, this paper constructs an action of an Artin group on the derived category of coherent sheaves of a smooth quasiprojective threefold containing a configuration of ruled surfaces described by a finite type Dynkin diagram. The action extends over deformations of the threefold via a compatible action of the corresponding reflection group on the base of its deformation space. All finite type Dynkin diagrams are realized.

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Derived category automorphisms from mirror symmetry

Cited by 73 publications

References 36 publications

$$\mathbb{C}^2/\mathbb{Z}_{n}$$ Fractional Branes and Monodromy

$$\mathbb{C}^2/\mathbb{Z}_{n}$$ Fractional Branes and Monodromy

On the Cn/Zm fractional branes

Artin group actions on derived categories of threefolds

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