UMR 5582 - Laboratoire de mathématiques
Published on UMR 5582 - Laboratoire de mathématiques (https://www-fourier.univ-grenoble-alpes.fr)

Accueil > Hamid Ahmadinezhad

Hamid Ahmadinezhad [1]

Finite generation of Cox rings and relations among Fano 3-folds
星期一, 17 二月, 2014 - 10:30
Résumé : 

Minimal model program provides new insights for the classification of algebraic varieties, and in particular Fanos.
The next step is to study relations among Fano varieties. A particular, and classical, relation of this type is the rationality for a smooth,
or mildly singular, hypersurface $X_d\subset\mathbb{P}^n$ of degree $d$ for $d\leq n$ (still unknown in many cases).

 
In this talk, using the theory of Sarkisov program (a la Corti), I highlight a strong relation between the finite generation of certain
Cox rings and the existence of birational maps from a given Fano 3-fold. This provides an effective and systematic method of obtaining
birational maps between Mori fibre spaces or proving their non-existence (the birational rigidity in the extreme case). I will report
on joint projects with Anne-Sophie Kaloghiros and Francesco Zucconi for particular cases in both directions.
Thème de recherche : 
Algèbre et géométries
Salle : 
04

Source URL: https://www-fourier.univ-grenoble-alpes.fr/?q=zh-hans/content/hamid-ahmadinezhad

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[1] https://www-fourier.univ-grenoble-alpes.fr/?q=zh-hans/content/hamid-ahmadinezhad