Birational Geometry of Hypersurfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Birational Geometry of Hypersurfaces write by Andreas Hochenegger. This book was released on 2019-10-08. Birational Geometry of Hypersurfaces available in PDF, EPUB and Kindle. Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results. The aim of the school was to shed light on this vast area of research by concentrating on two main aspects: (1) Approaches focusing on (stable) rationality using deformation theory and Chow-theoretic tools like decomposition of the diagonal; (2) The connection between K3 surfaces, hyperkähler geometry and cubic fourfolds, which has both a Hodge-theoretic and a homological side. Featuring the beautiful lectures given at the school by Jean-Louis Colliot-Thélène, Daniel Huybrechts, Emanuele Macrì, and Claire Voisin, the volume also includes additional notes by János Kollár and an appendix by Andreas Hochenegger.
The Geometry of Cubic Hypersurfaces
The Geometry of Cubic Hypersurfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Geometry of Cubic Hypersurfaces write by Daniel Huybrechts. This book was released on 2023-06-30. The Geometry of Cubic Hypersurfaces available in PDF, EPUB and Kindle. Cubic hypersurfaces are described by almost the simplest possible polynomial equations, yet their behaviour is rich enough to demonstrate many of the central challenges in algebraic geometry. With exercises and detailed references to the wider literature, this thorough text introduces cubic hypersurfaces and all the techniques needed to study them. The book starts by laying the foundations for the study of cubic hypersurfaces and of many other algebraic varieties, covering cohomology and Hodge theory of hypersurfaces, moduli spaces of those and Fano varieties of linear subspaces contained in hypersurfaces. The next three chapters examine the general machinery applied to cubic hypersurfaces of dimension two, three, and four. Finally, the author looks at cubic hypersurfaces from a categorical point of view and describes motivic features. Based on the author's lecture courses, this is an ideal text for graduate students as well as an invaluable reference for researchers in algebraic geometry.
Birational Geometry of Foliations
Birational Geometry of Foliations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Birational Geometry of Foliations write by Marco Brunella. This book was released on 2015-03-25. Birational Geometry of Foliations available in PDF, EPUB and Kindle. The text presents the birational classification of holomorphic foliations of surfaces. It discusses at length the theory developed by L.G. Mendes, M. McQuillan and the author to study foliations of surfaces in the spirit of the classification of complex algebraic surfaces.
Automorphisms in Birational and Affine Geometry
Automorphisms in Birational and Affine Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Automorphisms in Birational and Affine Geometry write by Ivan Cheltsov. This book was released on 2014-06-11. Automorphisms in Birational and Affine Geometry available in PDF, EPUB and Kindle. The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geometry where, in both cases, the automorphism group is often infinite dimensional. The collection covers a wide range of topics and is intended for researchers in the fields of classical algebraic geometry and birational geometry (Cremona groups) as well as affine geometry with an emphasis on algebraic group actions and automorphism groups. It presents original research and surveys and provides a valuable overview of the current state of the art in these topics. Bringing together specialists from projective, birational algebraic geometry and affine and complex algebraic geometry, including Mori theory and algebraic group actions, this book is the result of ensuing talks and discussions from the conference “Groups of Automorphisms in Birational and Affine Geometry” held in October 2012, at the CIRM, Levico Terme, Italy. The talks at the conference highlighted the close connections between the above-mentioned areas and promoted the exchange of knowledge and methods from adjacent fields.
Birational Geometry of Algebraic Varieties
Birational Geometry of Algebraic Varieties - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Birational Geometry of Algebraic Varieties write by Janos Kollár. This book was released on 2010-03-24. Birational Geometry of Algebraic Varieties available in PDF, EPUB and Kindle. One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.
