On the Lüroth problem for real varieties - TIB AV-Portal

On the Lüroth problem for real varieties

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Centre International de Rencontres Mathématiques (CIRM)

Benoist, Olivier

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Title

On the Lüroth problem for real varieties

Title of Series

THEMATIC MONTH: Complex Geometry

Part Number

12

Number of Parts

29

Author

Benoist, Olivier

Contributors

Hennenfent, Guillaume (Filmmaker)

Wittenberg, Olivier

License

CC Attribution - NonCommercial - NoDerivatives 2.0 Generic:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.

Identifiers

10.5446/53777 (DOI)

Publisher

Centre International de Rencontres Mathématiques (CIRM)

Release Date

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Genre

Conference/Talk

Abstract

The Lüroth problem asks whether every unirational variety is rational. Over the complex numbers, it has a positive answer for curves and surfaces, but fails in higher dimensions. In this talk, I will consider the Lüroth problem for real algebraic varieties that are geometrically rational, and explain a counterexample not accounted for by the topology of the real locus or by unramified cohomology.

Series

THEMATIC MONTH: Complex Geometry12 / 29

1

55:55

Topics on K3 surfaces - Lecture 1: K3 surfaces in the Enriques Kodaira classification and examples

2

56:32

Topics on K3 surfaces - Lecture 2: Kummer surfaces

3

1:04:16

Topics on K3 surfaces - Lecture 3: Basic properties of K3 surfaces

4

56:17

Topics on K3 surfaces - Lecture 4: Nèron-Severi group and automorphisms

5

1:01:57

Topics on K3 surfaces - Lecture 5: Finite automorphism groups

6

55:01

Topics on K3 surfaces - Lecture 6: Classification

7

53:25

Apriori estimates for scalar curvature type equations on compact Kähler manifolds

8

46:44

Moduli of algebraic varieties

9

51:49

Algebraicity of the metric tangent cones

10

53:43

Kodaira dimension of algebraic fiber spaces over abelian varieties or projective surfaces

11

50:33

Pluripotential Kähler-Ricci flows

12

1:00:56

On the Lüroth problem for real varieties

13

58:40

Absolute sets and the Decomposition Theorem

14

1:04:49

Arithmetic of rank one local systems

15

53:48

On the B-Semiampleness Conjecture

16

1:02:35

Stably irrational hypersurfaces of small slopes

17

1:08:14

Improved bounds for jet differential operators and the Kobayashi conjecture

18

55:23

Arithmetic and algebraic hyperbolicity

19

58:22

A Grassmannian technique and the Kobayashi Conjecture

20

1:01:55

Isotriviality for families given by regular foliations

21

1:08:04

Special manifolds, the core fibration, rational and entire curves

22

53:56

Construction of lattices defining fake projective planes - Lecture 1

23

1:02:29

Construction of lattices defining fake projective planes - Lecture 2

24

56:54

Construction of lattices defining fake projective planes - Lecture 3

25

52:23

Construction of lattices defining fake projective planes - Lecture 4

26

57:52

Construction of lattices defining fake projective planes - Lecture 5

27

1:03:18

Construction of lattices defining fake projective planes - Lecture 6

28

44:55

Construction of lattices defining fake projective planes - Lecture 7

29

37:59

Construction of lattices defining fake projective planes - Lecture 8

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