201104.4315v1 Extremal Kahler metrics on blow-ups of parabolic ruled surfaces精品.pdfVIP

1 1 0 2 r p A 1 2 ] G ¨ D EXTREMAL KAHLER METRICS ON BLOW-UPS OF PARABOLIC . RULED SURFACES h t a m CARL TIPLER [ 1 v 5 ABSTRACT. The aim of this paper is to provide new examples of extremal 1 K¨ahler metrics with non-constant scalar curvature on blown-up ruled sur- 3 faces. 4 . 4 1. INTRODUCTION 0 1 The aim of this text is to construct new examples of extremal Kahler¨ metrics 1 0 with non-constant scalar curvature. These constructions will concern iterated 2 blow-ups of minimal models of ruled surfaces. Extremal K¨ahler metrics on y ruled surfaces have already been studied. The first examples come from a r work of Calabi ([C1]) who gave such explicit metrics on rational surfaces. o e The work of Tønnesen ([T]) gives extremal metrics on ruled surfaces, namely h the pseudo-Hirzebruch ruled surfaces. T In a joint work of Arezzo, Pacard and Singer (see [AP1], [AP2] and [APS]), r e a theory of gluing is developed in order to construct extremal metrics on the b blow-up of a manifold which already carries an extremal metric. This en- m ables one to construct extremal metrics on blow-ups of Hirzebruch or pseudo- u Hirzebruch surfaces from the examples of Calabi and Tønnesen. The work N presented here will use the gluing theory developed by Arezzo Pacard and / m Singer in another way so that the metrics ob