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Circle of Sarkisov Links on a Fano 3-Fold

Part of: Birational geometry

Published online by Cambridge University Press:  23 May 2016

Hamid Ahmadinezhad  and
Francesco Zucconi
Hamid Ahmadinezhad
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK ([email protected])
Francesco Zucconi
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studî Udine, Via delle Scienze, 206, 33100 Udine, Italy ([email protected])
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Abstract

For a general Fano 3-fold of index 1 in the weighted projective space ℙ(1, 1, 1, 1, 2, 2, 3) we construct two new birational models that are Mori fibre spaces in the framework of the so-called Sarkisov program. We highlight a relation between the corresponding birational maps, as a circle of Sarkisov links, visualizing the notion of relations in the Sarkisov program.

Keywords

birational automorphismFano varietiesSarkisov programvariation of geometric invariant theory

MSC classification

Secondary: 14E05: Rational and birational maps 14E30: Minimal model program (Mori theory, extremal rays) 14E07: Birational automorphisms, Cremona group and generalizations 14E08: Rationality questions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 1 , February 2017 , pp. 1 - 16
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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