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Fano varieties and Cremona groupsучебный курс
- Автор: Прохоров Ю.Г.
- Год создания: 2012
- Организация: МГУ имени М.В. Ломоносова
- Курс на иностранном языке
- Описание: 35th Autumn School in Algebraic Geometry Subgroups of Cremona groups Lukecin, Poland, September 23 -- September 29, 2012 Teachers: Yuri Prokhorov (Moscow) and Jeremy Blanc (Basel) Abstract: The subject of the school concerns finite subgroups of groups of birational transformations of projective spaces. This topic is classical and goes back to the last quarter of the 19th century and it has its vivid renaissance in the last two decades. Two series of lectures will survey the most recent methods and results in this field. The lectures of Yuri Prokhorov will focus on Fano manifolds and will provide an introduction to Mori theory. The lectures of Jeremy Blanc will concentrate on finite subgroups of birational transformations of the plane. Prerequisites: Basic knowledge of algebraic geometry. Program of the school: There will be 2 lectures each morning, 90 min each, followed by 90 min excercise session in the afternoon and contributed talks in the evening. Fano varieties and Cremona groups, by Yuri Prokhorov. Abstract (subject to change): The aim of this course is to present basic results on Fano varieties and give examples; it will also serve as a preparation for the course of Jeremy Blanc. The following topics will be covered: Basic properties of Fano varieties. Examples. Del Pezzo surfaces. Introduction to Mori theory, Fano varieties in the framework of the MMP. Three-dimensional MMP. Outline of Mori-Mukai classification. Introduction to Sarkisov links. Examples. Outline of Iskovskikh classification (three-dimensional case). Application to the classification of finite subgroups of Cremona groups. Readings to Prokhorov's lectures: Exercises: Fano Varieties Fano varieties: Iskovskikh, Prokhorov, Fano varieties. Algebraic geometry, V, 1-247, Encyclopaedia Math. Sci., 47, Springer, Berlin, 1999 Mukai, New developments in the theory of Fano threefolds: vector bundle method and moduli problems Sugaku Expositions 15 (2002), no. 2, 125-150, available at http://www.math.nagoya-u.ac.jp/~mukai/ Del Pezzo surfaces: Manin, Cubic forms: algebra, geometry, arithmetic. North-Holland Mathematical Library, Vol. 4. 1974 [Ch. 4, sect. 23-26] Smith, Karen E.; Corti, Alessio Rational and nearly rational varieties. Cambridge Studies in Advanced Mathematics, 92. Cambridge University Press, Cambridge, 2004 Dolgachev, Classical algebraic geometry: a modern view, available at http://www.math.lsa.umich.edu/~idolga/, [Ch. 8]
- Добавил в систему: Прохоров Юрий Геннадьевич