Existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes

Authors:	F. Campana B. Kreuß ler

Affiliation:	Department of Mathematics, Université de Nancy, F--54506 Vandouvre les Nancy, France ; Department of Mathematics, Universität Kaiserslautern, D--67653 Kaiserslautern, Germany

Abstract:	We prove the existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes $4 mathbb{C}mathbb{P}^2$ . These are the first examples of twistor spaces of algebraic dimension two over a simply connected Riemannian four-manifold with positive scalar curvature. For this purpose we develop a method to distinguish between twistor spaces of algebraic dimension one and two by looking at the order of a certain point in the Picard group of an elliptic curve.

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