By Aleksandr Pukhlikov

ISBN-10: 0821894765

ISBN-13: 9780821894767

Birational tension is a notable and mysterious phenomenon in higher-dimensional algebraic geometry. It seems that definite ordinary households of algebraic forms (for instance, three-d quartics) belong to an analogous category kind because the projective area yet have greatly various birational geometric homes. particularly, they admit no non-trivial birational self-maps and can't be fibred into rational forms by means of a rational map. The origins of the idea of birational tension are within the paintings of Max Noether and Fano; even though, it used to be purely in 1970 that Iskovskikh and Manin proved birational superrigidity of quartic three-folds. This publication provides a scientific exposition of, and a entire creation to, the idea of birational tension, providing in a uniform approach, rules, ideas, and effects that to this point may perhaps in basic terms be present in magazine papers. the new speedy development in birational geometry and the widening interplay with the neighboring parts generate the transforming into curiosity to the rigidity-type difficulties and effects. The e-book brings the reader to the frontline of present examine. it really is basically addressed to algebraic geometers, either researchers and graduate scholars, yet is usually obtainable for a much wider viewers of mathematicians acquainted with the fundamentals of algebraic geometry

**Read or Download Birationally Rigid Varieties: Mathematical Analysis and Asymptotics PDF**

**Similar algebraic geometry books**

Backbone identify: creation to moduli difficulties and orbit areas.

**New PDF release: Higher-Dimensional Algebraic Geometry**

Higher-Dimensional Algebraic Geometry reviews the type concept of algebraic forms. This very energetic zone of study continues to be constructing, yet an awesome volume of information has amassed over the last 20 years. The author's objective is to supply an simply obtainable creation to the topic.

**Hilbert - download pdf or read online**

Now in new alternate paper variations, those vintage biographies of 2 of the best twentieth Century mathematicians are being published below the Copernicus imprint. those noteworthy debts of the lives of David Hilbert and Richard Courant are heavily comparable: Courant's tale is, in lots of methods, obvious because the sequel to the tale of Hilbert.

**Foliation Theory in Algebraic Geometry - download pdf or read online**

That includes a mix of unique study papers and entire surveys from a global workforce of major researchers within the thriving fields of foliation idea, holomorphic foliations, and birational geometry, this booklet provides the lawsuits of the convention "Foliation concept in Algebraic Geometry," hosted by means of the Simons starting place in big apple urban in September 2013.

- A geometric introduction to K-theory [Lecture notes]
- Computational Algebraic Geometry (Progress in Mathematics)
- Spaces of Homotopy Self-Equivalences: A Survey
- Computational Commutative Algebra
- Abelian varieties and the Fourier transform
- Fundamentals of the Theory of Operator Algebras, Vol. 2: Advanced Theory

**Additional resources for Birationally Rigid Varieties: Mathematical Analysis and Asymptotics**

**Example text**

The ﬁrst attempts to apply this method to varieties of higher degree (the complete intersection V2·3 ⊂ P5 of a quadric and a cubic [I80]) and singular varieties (three-dimensional quartics with a double point) were not completed; see Notes and references for Chapter 2. At the same time, from the geometric point of view, varieties of higher degree are more interesting; there are not too many Fano varieties of small degree. It seemed for a long time that the method developed in [IM] makes it possible to obtain isolated results of exceptional type only [I80], whereas the majority of Fano varieties (the more so, in higher dimensions) are out of reach for this approach.

1. CANONICAL ADJUNCTION 43 Proof. This is obvious: we have just listed the possible cases.

The Sarkisov theorem showed once again that the very rationality problem needs to be modiﬁed to develop an adequate higher-dimensional theory, and conﬁrmed the direction, in which this generalization was to be sought. 3. The Sarkisov theorem on conic bundles. Let S be a smooth projective variety of dimension dim S ≥ 2, ρ : E → S an (algebraic) vector bundle of rank 3, ρ : P(E) → S its projectivization, that is, a locally trivial P2 -bundle over S. A hypersurface V ⊂ P(E), equipped with the natural projection π : V → S, π = ρ | V , is called a conic bundle over S, if every ﬁbre π −1 (s) ⊂ P2 = ρ−1 (s) is a conic in P2 .

### Birationally Rigid Varieties: Mathematical Analysis and Asymptotics by Aleksandr Pukhlikov

by Kenneth

4.1

- Advanced Euclidean Geometry - download pdf or read online
- Algebraic and Complex Geometry: In Honour of Klaus Hulek's - download pdf or read online

Categories: Algebraic Geometry