# Instanton moduli as a novel map from tori to K3-surfaces

@article{Braam1992InstantonMA, title={Instanton moduli as a novel map from tori to K3-surfaces}, author={Peter J. Braam and Antony Maciocia and Andrey N. Todorov}, journal={Inventiones mathematicae}, year={1992}, volume={108}, pages={419-451} }

A map is constructed from the moduli of hyper-Kähler tori to hyper-Kähler K3 surfaces which does not coincide with the Kummer map. The map takes a torus to the moduli space of SO(3) connections on a bundle with nontrivial first Stiefel-Whitney class and first Pontrjagin class equal to −4. This map is shown to intersect the Kummer moduli and also certain subvarieties of singular K3 surfaces. Our map is shown to satisfy the local Torelli theorem, and the K3-surfaces in its image are shown to…

## 13 Citations

Instantons and mirror K3 surfaces

- Mathematics
- 1992

The instanton moduli space of a real 4-dimensional torus is an 8-dimensional Calabi-Yau manifold. Associated to this Calabi-Yau manifold are two (singular) K3 surfaces, one a quotient, the other a…

Instanton moduli for T3 × ℝ

- Physics
- 1995

We review the specific problems that arise when studying instantons on a torus. We discuss how the Nahm transformation shows that no exact charge one instanton on T 4 can exist. However, taking one…

The determinant line bundle over moduli spaces of instantons on abelian surfaces

- Mathematics
- 1994

We study the determinant line bundle over moduli space of stable bundles on abelian surfaces. We evaluate their analytic torsions. We extend Mukai's version of the Parseval Theorem to L 2 metrics on…

ZERO-DIMENSIONAL SCHEMES ON ABELIAN SURFACES

- Physics
- 1994

The moduli spaces of semistable torsion-free sheaves with c 1 = 0 and c 2 = ?2 and ?3 over a principally polarised complex torus are described explicitly in terms of zero-dimensional subschemes of…

Nahm dualities on the torus - a synthesis

- Physics
- 1999

Abstract We give a unified description of self-dual SU(2) gauge fields on tori of size lt×ls3, based on a mixture of analytical and numerical methods using the Nahm transformation, extended to the…

Generalized Fourier-Mukai transforms.

- Mathematics
- 1996

The paper sets out a generalized framework for Fourier-Mukai transforms and illustrates their use via vector bundle transforms. A Fourier-Mukai transform is, roughly, an isomorphism of derived…

Gieseker stability and the Fourier-Mukai transform for Abelian surfaces

- Mathematics
- 1996

The preservation properties of Gieseker stability and semistability under the Fourier transform of Mukai are discussed. A fundamental lemma is proved describing the degree of sheaves whose Fourier…

Tunneling through sphalerons: the O(3) σ-model on a cylinder

- Physics
- 1994

Abstract We construct all instantons for the O(3) σ-model on a cylinder, known not to exist on a finite time interval. We show that the widest instantons go through sphalerons. A re-interpretation of…

Instantons from over-improved cooling

- Physics
- 1993

Lattice artefacts are used, through modified lattice actions, as a tool to find the largest instantons in a toroidal geometry [0,L]^3X[0,T] for T to infinity. It is conjectured that the largest…

Nahm gauge fields for the torus

- Physics
- 1998

Abstract We present the exact expression for the Nahm gauge field associated to a SU ( N ) charge one self-dual gauge field on T 3 × R . The result implies that the size of the instanton is…

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