Cremona transformations and diffeomorphisms of surfaces

János Kollár; Frédéric Mangolte

doi:10.1016/j.aim.2009.03.020

Cremona transformations and diffeomorphisms of surfaces

János Kollár, Frédéric Mangolte

Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We show that the action of Cremona transformations on the real points of quadrics exhibits the full complexity of the diffeomorphisms of the sphere, the torus, and of all non-orientable surfaces. The main result says that if X is rational, then Aut (X), the group of algebraic automorphisms, is dense in Diff (X), the group of self-diffeomorphisms of X.

Original language	English (US)
Pages (from-to)	44-61
Number of pages	18
Journal	Advances in Mathematics
Volume	222
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2009.03.020
State	Published - Sep 10 2009

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Automorphism group
Diffeomorphism group
Mapping class group
Rational surface
Real algebraic surface

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10.1016/j.aim.2009.03.020

Cite this

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title = "Cremona transformations and diffeomorphisms of surfaces",

abstract = "We show that the action of Cremona transformations on the real points of quadrics exhibits the full complexity of the diffeomorphisms of the sphere, the torus, and of all non-orientable surfaces. The main result says that if X is rational, then Aut (X), the group of algebraic automorphisms, is dense in Diff (X), the group of self-diffeomorphisms of X.",

keywords = "Automorphism group, Diffeomorphism group, Mapping class group, Rational surface, Real algebraic surface",

author = "J{\'a}nos Koll{\'a}r and Fr{\'e}d{\'e}ric Mangolte",

note = "Funding Information: Partial financial support for J.K. was provided by the NSF under grant number DMS-0500198. The research of F.M. was partially supported by the ANR grant “JCLAMA” of the French “Agence Nationale de la Recherche.” He also benefited from the hospitality of Princeton University.",

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AU - Mangolte, Frédéric

N1 - Funding Information: Partial financial support for J.K. was provided by the NSF under grant number DMS-0500198. The research of F.M. was partially supported by the ANR grant “JCLAMA” of the French “Agence Nationale de la Recherche.” He also benefited from the hospitality of Princeton University.

PY - 2009/9/10

Y1 - 2009/9/10

N2 - We show that the action of Cremona transformations on the real points of quadrics exhibits the full complexity of the diffeomorphisms of the sphere, the torus, and of all non-orientable surfaces. The main result says that if X is rational, then Aut (X), the group of algebraic automorphisms, is dense in Diff (X), the group of self-diffeomorphisms of X.

AB - We show that the action of Cremona transformations on the real points of quadrics exhibits the full complexity of the diffeomorphisms of the sphere, the torus, and of all non-orientable surfaces. The main result says that if X is rational, then Aut (X), the group of algebraic automorphisms, is dense in Diff (X), the group of self-diffeomorphisms of X.

KW - Automorphism group

KW - Diffeomorphism group

KW - Mapping class group

KW - Rational surface

KW - Real algebraic surface

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JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

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Cremona transformations and diffeomorphisms of surfaces

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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