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.
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. A detailed introduction to cubic hypersurfaces, applying diverse techniques to a central class of algebraic varieties.
Algebraic Geometry and Number Theory
Algebraic Geometry and Number Theory - 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 Algebraic Geometry and Number Theory write by Hussein Mourtada. This book was released on 2017-05-16. Algebraic Geometry and Number Theory available in PDF, EPUB and Kindle. This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.
Birational Geometry of Hypersurfaces
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.
Cubic Forms
Cubic Forms - 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 Cubic Forms write by Yu.I. Manin. This book was released on 1986-02-01. Cubic Forms available in PDF, EPUB and Kindle. Since this book was first published in English, there has been important progress in a number of related topics. The class of algebraic varieties close to the rational ones has crystallized as a natural domain for the methods developed and expounded in this volume. For this revised edition, the original text has been left intact (except for a few corrections) and has been brought up to date by the addition of an Appendix and recent references.The Appendix sketches some of the most essential new results, constructions and ideas, including the solutions of the Luroth and Zariski problems, the theory of the descent and obstructions to the Hasse principle on rational varieties, and recent applications of K-theory to arithmetic.
