Fourier¿Mukai and Nahm Transforms in Geometry and Mathematical Physics

Bartocci, Claudio; Bruzzo, Ugo; Ruipérez, Daniel Hernández

doi:10.1007/b11801

Cited by 100 publications

(240 citation statements)

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“…When X and Y are smooth, our definition is weaker than the usual one given by Bondal and Orlov (see [2]). Thus, Theorem 3.6 improves a result of Bondal and Orlov [6, Thm.…”

Section: Strongly Simple Objects and Spanning Classesmentioning

confidence: 94%

“…We expect that Proposition 2.16 could be a useful tool for the study of the moduli spaces of relatively semistable sheaves on X → S with respect to a suitable relative ample divisor following [3,2,9,15], and for the study of the derived category of X generalising [10].…”

Section: Introductionmentioning

confidence: 99%

“…We would like to thank the authors of the forthcoming book [2] for sharing with us their notes and to the anonymous referees for comments and suggestions which helped us to improve the manuscript. Ana Cristina López Martín would also like to thank Miles Reid for useful comments and for his warm welcome in Warwick.…”

mentioning

confidence: 99%

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Relative integral functors for singular fibrations and singular partners

Ruipérez¹,

Martín²,

Salas³

2009

J. Eur. Math. Soc.

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Abstract. We study relative integral functors for singular schemes and characterise those which preserve boundedness and those which have integral right adjoints. We prove that a relative integral functor is an equivalence if and only if its restriction to every fibre is an equivalence. This allows us to construct a non-trivial auto-equivalence of the derived category of an arbitrary genus one fibration with no conditions on either the base or the total space and getting rid of the usual assumption of irreducibility of the fibres. We also extend to Cohen-Macaulay schemes the criterion of Bondal and Orlov for an integral functor to be fully faithful in characteristic zero and give a different criterion which is valid in arbitrary characteristic. Finally, we prove that for projective schemes both the Cohen-Macaulay and the Gorenstein conditions are invariant under Fourier-Mukai functors.

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“…When X and Y are smooth, our definition is weaker than the usual one given by Bondal and Orlov (see [2]). Thus, Theorem 3.6 improves a result of Bondal and Orlov [6, Thm.…”

Section: Strongly Simple Objects and Spanning Classesmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

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Relative integral functors for singular fibrations and singular partners

Ruipérez¹,

Martín²,

Salas³

2009

J. Eur. Math. Soc.

Self Cite

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“…As L is harmonic, 36) periodic and odd, it has an expansion in terms of Bessel-MacDonald functions of the form…”

Section: Jhep05(2014)055mentioning

confidence: 99%

“…An important tool in the theory of hyperholomorphic bundles and connections is the generalized Nahm transform [29][30][31][32][33][34][35][36], which relates hyperholomorphic bundles on certain dual pairs of hyperKähler manifolds (M, X ). The duality typically proceeds by defining a family of Dirac operators / D x on M parameterized by a point x ∈ X and then constructing an hyperholomorphic connection on X from the kernel of the Dirac operators.…”

Section: Jhep05(2014)055mentioning

confidence: 99%

tt * geometry in 3 and 4 dimensions

Cecotti

Gaiotto

Vafa

2014

J. High Energ. Phys.

163

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Abstract:We consider the vacuum geometry of supersymmetric theories with 4 supercharges, on a flat toroidal geometry. The 2 dimensional vacuum geometry is known to be captured by the tt * geometry. In the case of 3 dimensions, the parameter space is (T 2 × R) N and the vacuum geometry turns out to be a solution to a generalization of monopole equations in 3N dimensions where the relevant topological ring is that of line operators. We compute the generalization of the 2d cigar amplitudes, which lead to S 2 ×S 1 or S 3 partition functions which are distinct from the supersymmetric partition functions on these spaces, but reduce to them in a certain limit. We show the sense in which these amplitudes generalize the structure of 3d Chern-Simons theories and 2d RCFT's. In the case of 4 dimensions the parameter space is of the form X M,N = (T 3 × R) M × T 3N , and the vacuum geometry is a solution to a mixture of generalized monopole equations and generalized instanton equations (known as hyper-holomorphic connections). In this case the topological rings are associated to surface operators. We discuss the physical meaning of the generalized Nahm transforms which act on all of these geometries.

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Coherent systems on a nodal curve of genus one

Bhosle

2011

Mathematische Nachrichten

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Fourier¿Mukai and Nahm Transforms in Geometry and Mathematical Physics

Cited by 100 publications

References 0 publications

Relative integral functors for singular fibrations and singular partners

Relative integral functors for singular fibrations and singular partners

tt * geometry in 3 and 4 dimensions

Coherent systems on a nodal curve of genus one

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