Journal ArticleDOI
Anti Self‐Dual Yang‐Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles
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In this paper, a correspondance entre the geometries algebrique and the geometry differentielle des fibres vectoriels is presented, and a connexion irreductible d'Hermite-Einstein par rapport a metrique ω.Abstract:
On presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels. Soit une surface algebrique projective X qui a un plongement donne X≤CP N et soit ω une metrique de Kahler sur X dont la classe de cohomologie associee est duale a la classe de section d'hyperplan [H]. Un fibre sur X est stable, par rapport au plongement projectif, si et seulement si il admet une connexion irreductible d'Hermite-Einstein par rapport a la metrique ω. Cette connexion est alors uniqueread more
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References
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Principles of Algebraic Geometry
Phillip Griffiths,Joe Harris +1 more
TL;DR: In this paper, a comprehensive, self-contained treatment of complex manifold theory is presented, focusing on results applicable to projective varieties, and including discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex.
BookDOI
Multiple integrals in the calculus of variations
TL;DR: In this paper, a variational method in the theory of harmonic integrals has been proposed to solve the -Neumann problem on strongly pseudo-convex manifolds and parametric Integrals two-dimensional problems.
Journal ArticleDOI
The Yang-Mills equations over Riemann surfaces
Michael Atiyah,Raoul Bott +1 more
TL;DR: In this article, the Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory, and the main result is that this is a perfect 9 functional provided due account is taken of its gauge symmetry.
Journal ArticleDOI
Self-duality in four-dimensional Riemannian geometry
TL;DR: In this article, the authors present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis, and apply this to the self-dual Yang-Mills equations in Euclidean 4-space and compute the number of moduli for any compact gauge group.