Birationally Rigid Varieties PDF Download
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Author | : Aleksandr V. Pukhlikov |
Publisher | : American Mathematical Soc. |
Total Pages | : 378 |
Release | : 2013-05-15 |
Genre | : Mathematics |
ISBN | : 0821894765 |
Download Birationally Rigid Varieties Book in PDF, ePub and Kindle
Birational rigidity is a striking and mysterious phenomenon in higher-dimensional algebraic geometry. It turns out that certain natural families of algebraic varieties (for example, three-dimensional quartics) belong to the same classification type as the
Author | : A. V. Pukhlikov |
Publisher | : |
Total Pages | : 24 |
Release | : 2003 |
Genre | : |
ISBN | : |
Download Birationally Rigid Fano Varieties Book in PDF, ePub and Kindle
Author | : Aleksandr V. Pukhlikov |
Publisher | : |
Total Pages | : 36 |
Release | : 2004 |
Genre | : |
ISBN | : |
Download Birationally Rigid Varieties with a Pencil of Fano Double Covers Book in PDF, ePub and Kindle
Author | : A. V. Pukhlikov |
Publisher | : |
Total Pages | : 14 |
Release | : 1998 |
Genre | : |
ISBN | : |
Download Certain Examples of Birationally Rigid Varieties with a Pencil of Double Quadrics Book in PDF, ePub and Kindle
Author | : Renzo John Mullany |
Publisher | : |
Total Pages | : |
Release | : 2010 |
Genre | : |
ISBN | : |
Download Birationally Rigid Singular Fano Varieties Book in PDF, ePub and Kindle
Author | : Ivan Cheltsov |
Publisher | : American Mathematical Soc. |
Total Pages | : 130 |
Release | : 2017-02-20 |
Genre | : Mathematics |
ISBN | : 1470423162 |
Download Birationally Rigid Fano Threefold Hypersurfaces Book in PDF, ePub and Kindle
The authors prove that every quasi-smooth weighted Fano threefold hypersurface in the 95 families of Fletcher and Reid is birationally rigid.
Author | : Ivan Cheltsov |
Publisher | : Springer Nature |
Total Pages | : 882 |
Release | : 2023-05-23 |
Genre | : Mathematics |
ISBN | : 3031178599 |
Download Birational Geometry, Kähler–Einstein Metrics and Degenerations Book in PDF, ePub and Kindle
This book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and Pohang The conferences were focused on the following two related problems: • existence of Kähler–Einstein metrics on Fano varieties • degenerations of Fano varieties on which two famous conjectures were recently proved. The first is the famous Borisov–Alexeev–Borisov Conjecture on the boundedness of Fano varieties, proved by Caucher Birkar (for which he was awarded the Fields medal in 2018), and the second one is the (arguably even more famous) Tian–Yau–Donaldson Conjecture on the existence of Kähler–Einstein metrics on (smooth) Fano varieties and K-stability, which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song Sun. The solutions for these longstanding conjectures have opened new directions in birational and Kähler geometries. These research directions generated new interesting mathematical problems, attracting the attention of mathematicians worldwide. These conferences brought together top researchers in both fields (birational geometry and complex geometry) to solve some of these problems and understand the relations between them. The result of this activity is collected in this book, which contains contributions by sixty nine mathematicians, who contributed forty three research and survey papers to this volume. Many of them were participants of the Moscow–Shanghai–Pohang conferences, while the others helped to expand the research breadth of the volume—the diversity of their contributions reflects the vitality of modern Algebraic Geometry.
Author | : Fedor Bogomolov |
Publisher | : Springer Science & Business Media |
Total Pages | : 316 |
Release | : 2009-11-03 |
Genre | : Mathematics |
ISBN | : 0817649344 |
Download Cohomological and Geometric Approaches to Rationality Problems Book in PDF, ePub and Kindle
Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry. This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties. This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems. Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Böhning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov
Author | : Ivan Cheltsov |
Publisher | : Springer |
Total Pages | : 509 |
Release | : 2014-06-11 |
Genre | : Mathematics |
ISBN | : 3319056816 |
Download Automorphisms in Birational and Affine Geometry Book 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.
Author | : Alessio Corti |
Publisher | : Cambridge University Press |
Total Pages | : 364 |
Release | : 2000-07-27 |
Genre | : Mathematics |
ISBN | : 9780521636414 |
Download Explicit Birational Geometry of 3-folds Book in PDF, ePub and Kindle
This volume, first published in 2000, is an integrated suite of papers centred around applications of Mori theory to birational geometry.