Calabi-You流形及相关几何

English | PDF (True) | 2003 | 245 Pages | ISBN : 3540440593 | 22 MB

Each summer since 1996,algebraic geometers and algebraists in Norway have organised a summer school in Nordfjordeid, a small place in the western part of Norway. In addition to the beauty of the place, located between the mountains, close to the fjord and not far from the Norway's largest glacier, a reason for going there is that Sophus Lie was born and spent his few first years in Nordfjordeid, so it has a flavour of both the exotic and pilgrimage. It is also convenient: the municipality of Eid has created a conference centre named after Sophus Lie, aimed at attracting activities to fillthe summer term of the local boarding school. The summer schools are a joint effort of the four universities in Norway - the universities of Tromse, Trondheim, Bergen and Oslo. They are pri- marily meant as training for Norwegiangraduate students, but have over the years attracted increasing numbers ofstudents from other parts of the world, adding the value of being international to the schools. The themes of the schools have been varied, but build around some cen- tral topics in contemporary mathematics. The format of the school has by now become tradition - three international experts giving independent, but certainly connected, series of talks with exercise sessions in the evening, over five or six days. In 2001 the organising committee consisted of Stein Arild Stromme from the University of Bergen, Loren Olson from the University of Tromse, and Kristian Ranestad and Geir Ellingsrud from the University of Oslo. We wanted to make a summer school giving the students insight in some of the new interactions between differential and algebraic geometry. The three topics wefinally chose, Riemannian holonomy and calibrated geometry, Calabi-Yau manifolds and mirror symmetry, and Compact hyperkiihler manifolds, are parts of the fascinating current development of mathematics, and we think they illustrate well the modern interplay between differential and algebraic geometry. Wewerefortunate enough to get positive answers when weasked Dominic Joyce, Mark Gross and Daniel Huybrechts to give the courses, and we are thankful for the great job the three lecturers did, both on stage in Nord- fjordeid and by writing up the nice notes which have now developed into this book. Geir Ellingsrud

English | PDF（True）| 2003 | 245页| ISBN:3540440593 | 22 MB自1996年以来，挪威的代数几何学家和代数学家每年夏天都会在挪威西部的一个小地方Nordfjordeid组织一所暑期学校。除了这个地方的美丽，它位于群山之间，靠近峡湾，距离挪威最大的冰川不远，去那里的一个原因是Sophus Lie出生并在Nordfjordeid度过了他的头几年，所以它既有异国情调，也有朝圣的味道。这也很方便：开斋节市政府创建了一个以Sophus Lie命名的会议中心，旨在吸引活动来填补当地寄宿学校的夏季学期。暑期学校是挪威四所大学——特罗姆塞大学、特隆赫姆大学、卑尔根大学和奥斯陆大学的联合项目。它们最初是为挪威研究生提供培训的，但多年来吸引了越来越多的来自世界其他地区的学生，为学校增添了国际化的价值。学校的主题各不相同，但都围绕着当代数学中的一些中心主题。学校的形式现在已经成为传统——三位国际专家在五到六天的时间里，在晚上进行一系列独立但肯定有联系的演讲和练习。2001年，组委会由卑尔根大学的Stein Arild Stromme、特罗姆塞大学的Loren Olson以及奥斯陆大学的Kristian Ranestad和Geir Ellingsrud组成。我们想开办一所暑期学校，让学生们了解微分几何和代数几何之间的一些新的相互作用。我们最终选择的三个主题，黎曼完整几何和校准几何、Calabi-You流形和镜像对称以及紧致hyperkiihler流形，是当前数学发展的一部分，我们认为它们很好地说明了微分几何和代数几何之间的现代相互作用。当我们邀请多米尼克·乔伊斯、马克·格罗斯和丹尼尔·胡布雷奇斯教授课程时，我们很幸运地得到了积极的回答，我们感谢三位讲师在北峡湾的舞台上所做的出色工作，以及他们写下的优美笔记，这些笔记现在已经发展成了这本书。盖尔·埃林斯鲁德

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