A Fourier-Mukai approach to spectral data for instantons

M  Jardim; A  Maciocia

A Fourier-Mukai approach to spectral data for instantons

M Jardim
, A Maciocia

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study SU(r) instantons on elliptic surfaces with a section and show that they are in one-one correspondence with spectral data consisting of a curve in the dual elliptic surface and a line bundle on that curve. We use relative Fourier-Mukai transforms to analyse their properties and, in the case of the K3 and abelian surface, we show that the moduli space of instantons has a natural Lagrangian fibration structure with respect to the canonical complex symplectic structures.

Original language	English
Pages (from-to)	221-235
Number of pages	15
Journal	Journal für die reine und angewandte Mathematik
Volume	563
Publication status	Published - Oct 2003

Keywords / Materials (for Non-textual outputs)

ELLIPTIC FIBRATIONS
ABELIAN SURFACES
VECTOR-BUNDLES
NAHM TRANSFORM
STABLE SHEAVES
MONOPOLES

Cite this

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title = "A Fourier-Mukai approach to spectral data for instantons",

abstract = "We study SU(r) instantons on elliptic surfaces with a section and show that they are in one-one correspondence with spectral data consisting of a curve in the dual elliptic surface and a line bundle on that curve. We use relative Fourier-Mukai transforms to analyse their properties and, in the case of the K3 and abelian surface, we show that the moduli space of instantons has a natural Lagrangian fibration structure with respect to the canonical complex symplectic structures.",

keywords = "ELLIPTIC FIBRATIONS, ABELIAN SURFACES, VECTOR-BUNDLES, NAHM TRANSFORM, STABLE SHEAVES, MONOPOLES",

author = "M Jardim and A Maciocia",

year = "2003",

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T1 - A Fourier-Mukai approach to spectral data for instantons

AU - Jardim, M

AU - Maciocia, A

PY - 2003/10

Y1 - 2003/10

N2 - We study SU(r) instantons on elliptic surfaces with a section and show that they are in one-one correspondence with spectral data consisting of a curve in the dual elliptic surface and a line bundle on that curve. We use relative Fourier-Mukai transforms to analyse their properties and, in the case of the K3 and abelian surface, we show that the moduli space of instantons has a natural Lagrangian fibration structure with respect to the canonical complex symplectic structures.

AB - We study SU(r) instantons on elliptic surfaces with a section and show that they are in one-one correspondence with spectral data consisting of a curve in the dual elliptic surface and a line bundle on that curve. We use relative Fourier-Mukai transforms to analyse their properties and, in the case of the K3 and abelian surface, we show that the moduli space of instantons has a natural Lagrangian fibration structure with respect to the canonical complex symplectic structures.

KW - ELLIPTIC FIBRATIONS

KW - ABELIAN SURFACES

KW - VECTOR-BUNDLES

KW - NAHM TRANSFORM

KW - STABLE SHEAVES

KW - MONOPOLES

M3 - Article

SN - 0075-4102

VL - 563

SP - 221

EP - 235

JO - Journal für die reine und angewandte Mathematik

JF - Journal für die reine und angewandte Mathematik

ER -

A Fourier-Mukai approach to spectral data for instantons

Abstract

Keywords / Materials (for Non-textual outputs)

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