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ВИДЕОТЕКА
Школа по алгебре и алгебраической геометрии
15–17 августа 2011 г., г. Екатеринбург

Бирациональная геометрия поверхностей и трехмерных многообразий

И. А. Чельцов

University of Edinburgh



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Аннотация: We will consider basics of birational geometry of surfaces and 3-folds with special regard to problems of rationality. The tentative plan of the lectures is the following:
Lecture 1. Blow ups, blow downs, canonical class, adjunction formula, rational surfaces, rationality criterion, quadric surfaces, cubic surfaces, two-dimensional Minimal Model Program, surfaces with a finite group action, surfaces over algebraically non-closed field of characteristic zero.
Lecture 2. Singularities of pairs, log canonical singularities, Kawamata log terminal singularities, mobile log pairs, canonical singularities, Nadel-Shokurov vanishing theorem, Inversion of Adjunction and its applications, Noether-Fano inequality, Pukhlikov inequality, Corti inequality.
Lecture 3. Non-rational surfaces over algebraically non-closed fields, non-rationality of smooth quartic 3-folds, finite subgroups in Cremona groups.

Список литературы
  1. Karen Smith, Joel Rosenberg, “Rational and Non-Rational Algebraic Varieties: Lectures of Janos Kollar”, arXiv: alg-geom/9707013
  2. Janos Kollar, Karen Smith, Alessio Corti, Rational and Nearly Rational Varieties, Cambridge University Press  mathscinet  zmath
  3. Janos Kollar, “Singularities of Pairs”, arXiv: alg-geom/9601026  mathscinet
  4. Aleksandr Pukhlikov, http://www.warwick.ac.uk/~masda/Unpub/CPR_book
  5. Alessio Corti, http://www.warwick.ac.uk/~masda/Unpub/CPR_book
  6. Igor Dolgachev, Vasily Iskovskikh, “Finite subgroups of the plane Cremona group”, arXiv: math/0610595  mathscinet
  7. Yuri Prokhorov, “Simple finite subgroups of the Cremona group of rank 3”, arXiv: 0908.0678  mathscinet
  8. Jeremy Blanc, “Finite abelian subgroups of the Cremona group of the plane”, arXiv: math/0610368  mathscinet
  9. Ivan Cheltsov, Constantin Shramov, “Five embeddings of one simple group”, arXiv: 0910.1783  mathscinet

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