SPACE AUT

Birational geometry and polynomial automorphisms of the affine space

 Coordinatore THE UNIVERSITY OF WARWICK 

 Organization address address: Kirby Corner Road - University House -
city: COVENTRY
postcode: CV4 8UW

contact info
Titolo: Dr.
Nome: Peter
Cognome: Hedges
Email: send email
Telefono: +44 24 7652 3716
Fax: +44 24 7652 4991

 Nazionalità Coordinatore United Kingdom [UK]
 Totale costo 0 €
 EC contributo 237˙684 €
 Programma FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
 Code Call FP7-PEOPLE-IEF-2008
 Funding Scheme MC-IEF
 Anno di inizio 2009
 Periodo (anno-mese-giorno) 2009-09-01   -   2011-08-31

 Partecipanti

# participant  country  role  EC contrib. [€] 
1    THE UNIVERSITY OF WARWICK

 Organization address address: Kirby Corner Road - University House -
city: COVENTRY
postcode: CV4 8UW

contact info
Titolo: Dr.
Nome: Peter
Cognome: Hedges
Email: send email
Telefono: +44 24 7652 3716
Fax: +44 24 7652 4991

UK (COVENTRY) coordinator 237˙684.38

Mappa


 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

sarkisov    right    birational    dimension    dimensional    sup    minimal    automorphisms    shestakov    umirbaev    factorization    group    tame    mori    proof    obtain   

 Obiettivo del progetto (Objective)

'In contrast with the 2-dimensional case, the study of automorphisms of C³ is still in its early beginnings. The most striking recent result is probably the proof by Shestakov and Umirbaev that a large class of automorphisms of C³ is non tame. Unfortunately their proof is based on tricky calculations and lacks conceptuality. On the other hand, Mori theory has emerged since the 1980s as the right framework to study birational maps in higher dimension, of which automorphisms of C³ are special cases. However up to now the known factorization algorithm ("Sarkisov program") has been essentially applied to varieties with a small group of birational selfmaps (typically a smooth 3-dimensional quartic, where one thus obtains an irrationality criterion). Very recently, Hacon and McKernan had made an announcement that the Sarkisov program in any dimension follows as a corollary from their major breakthrough; however their result is still very theoretical. We believe, and this is the first main objective of our proposal, that in the case of polynomial automorphisms one can modify the available proofs to obtain a canonical factorization by mean of steps in the logarithmic Minimal Model Program, and that this factorization could be computable in practice. Based partially on the elementary case of surfaces, and partially on explicit computations for automorphisms of low degree, our conviction is that the right point of view is to look for links not between Mori fiber spaces but between compactifications of C³ with a minimal number of irreducible components on the boundary. Among expected consequences we should mention a birational proof of the relations in the tame group in dimension 3 (which available proof depends on the "black box" of Shestakov and Umirbaev), and obtain some natural candidates to generate the automorphism group of C³.'

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