Mori dream spaces and birational rigidity of Fano 3-folds

Hamid Ahmadinezhad; Francesco Zucconi

doi:10.1016/j.aim.2016.01.008

Mori dream spaces and birational rigidity of Fano 3-folds

Hamid Ahmadinezhad^*, Francesco Zucconi

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

18 Citations (Scopus)

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Abstract

We highlight a relation between the existence of Sarkisov links and the finite generation of (certain) Cox rings. We introduce explicit methods to use this relation in order to prove birational rigidity statements. To illustrate, we complete the birational rigidity results of Okada for Fano complete intersection 3-folds in singular weighted projective spaces.

Original language	English
Pages (from-to)	410-445
Number of pages	36
Journal	Advances in Mathematics
Volume	292
Early online date	10 Feb 2016
DOIs	https://doi.org/10.1016/j.aim.2016.01.008
Publication status	Published - 9 Apr 2016

Keywords

Birational rigidity
Fano varieties
Mori dream spaces
Sarkisov program
Variation of geometric invariant theory

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abstract = "We highlight a relation between the existence of Sarkisov links and the finite generation of (certain) Cox rings. We introduce explicit methods to use this relation in order to prove birational rigidity statements. To illustrate, we complete the birational rigidity results of Okada for Fano complete intersection 3-folds in singular weighted projective spaces.",

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AU - Zucconi, Francesco

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AB - We highlight a relation between the existence of Sarkisov links and the finite generation of (certain) Cox rings. We introduce explicit methods to use this relation in order to prove birational rigidity statements. To illustrate, we complete the birational rigidity results of Okada for Fano complete intersection 3-folds in singular weighted projective spaces.

KW - Birational rigidity

KW - Fano varieties

KW - Mori dream spaces

KW - Sarkisov program

KW - Variation of geometric invariant theory

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DO - 10.1016/j.aim.2016.01.008

M3 - Article (Academic Journal)

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VL - 292

SP - 410

EP - 445

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Mori dream spaces and birational rigidity of Fano 3-folds

Abstract

Keywords

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