Explicity birational geometry of Fano 3folds of high index
We complete the analysis on the birational rigidity of quasismooth Fano 3fold deformation families appearing in the Graded Ring Database as a complete intersection. When such a deformation family X has Fano index at least 2 and is minimally embedded in a weighted projective space in codimension 2,...
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2022

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rrarticle1907816920220203T11:47:27Z Explicity birational geometry of Fano 3folds of high index Tiago Duarte Guerreiro (11510986) Other mathematical sciences not elsewhere classified Birational Geometry Fano 3folds Sarkisov Links Minimal Model Program Mathematical Sciences not elsewhere classified We complete the analysis on the birational rigidity of quasismooth Fano 3fold deformation families appearing in the Graded Ring Database as a complete intersection. When such a deformation family X has Fano index at least 2 and is minimally embedded in a weighted projective space in codimension 2, we determine which cyclic quotient singularity is a maximal centre. If a cyclic quotient singularity is a maximal centre, we construct a Sarkisov link to a nonisomorphic Mori fibre space or a birational involution. We define linear cyclic quotient singularities on X and prove that these are maximal centres by explicitly computing Sarkisov links centred at them. It turns out that each X has a linear cyclic quotient singularity leading to a new birational model. As a consequence, we show that if X is birationally rigid then its Fano index is 1. If the new birational model is a strict Mori fibre space, we determine its fibration type explicitly. In this case, a general member of X is birational to a del Pezzo fibration of degrees 1, 2 or 3 or to a conic bundle Y/S where S is a weighted projective plane with at most A<sub>2</sub> singularities. 20220203T11:47:27Z Text Thesis 10.26174/thesis.lboro.19078169.v1 https://figshare.com/articles/thesis/Explicity_birational_geometry_of_Fano_3folds_of_high_index/19078169 CC BYNCND 4.0 
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Other mathematical sciences not elsewhere classified Birational Geometry Fano 3folds Sarkisov Links Minimal Model Program Mathematical Sciences not elsewhere classified 
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Other mathematical sciences not elsewhere classified Birational Geometry Fano 3folds Sarkisov Links Minimal Model Program Mathematical Sciences not elsewhere classified Tiago Duarte Guerreiro Explicity birational geometry of Fano 3folds of high index 
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We complete the analysis on the birational rigidity of quasismooth Fano 3fold deformation families appearing in the Graded Ring Database as a complete intersection. When such a deformation family X has Fano index at least 2 and is minimally embedded in a weighted projective space in codimension 2, we determine which cyclic quotient singularity is a maximal centre. If a cyclic quotient singularity is a maximal centre, we construct a Sarkisov link to a nonisomorphic Mori fibre space or a birational involution. We define linear cyclic quotient singularities on X and prove that these are maximal centres by explicitly computing Sarkisov links centred at them. It turns out that each X has a linear cyclic quotient singularity leading to a new birational model. As a consequence, we show that if X is birationally rigid then its Fano index is 1. If the new birational model is a strict Mori fibre space, we determine its fibration type explicitly. In this case, a general member of X is birational to a del Pezzo fibration of degrees 1, 2 or 3 or to a conic bundle Y/S where S is a weighted projective plane with at most A2 singularities. 
format 
Default Thesis 
author 
Tiago Duarte Guerreiro 
author_facet 
Tiago Duarte Guerreiro 
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Tiago Duarte Guerreiro (11510986) 
title 
Explicity birational geometry of Fano 3folds of high index 
title_short 
Explicity birational geometry of Fano 3folds of high index 
title_full 
Explicity birational geometry of Fano 3folds of high index 
title_fullStr 
Explicity birational geometry of Fano 3folds of high index 
title_full_unstemmed 
Explicity birational geometry of Fano 3folds of high index 
title_sort 
explicity birational geometry of fano 3folds of high index 
publishDate 
2022 
url 
https://dx.doi.org/10.26174/thesis.lboro.19078169.v1 
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1796098668965658624 