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Theses

Sur les variétés de Fano obtenues par éclatement d'une courbe lisse dans une variété projective

Abstract : The purpose of this thesis is to classify the Fano manifolds X (namely manifolds whose anticanonical bundles are ample) obtained by blow-up along a smooth curve C in a complex projective manifold Y. By Mori theory, the Fano manifolds of Picard number grater than 1 have at least two morphisms called extremal contractions which send rational curves on the Fano manifold to points in its image. In our situation we can ensure the existence of an extremal contraction whose fibers intersect the exceptional divisor of the blow-up along C. For the case in which this another contraction is of fiber type, we give a complete classification of the pairs (Y,C) (we will need an additional assumption if the general fibers of the contraction are of dimension 1). If the another contraction is birational, we have only partial results which show nevertheless that various situations can be possible.
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Theses
File URL :
http://docnum.univ-lorraine.fr/prive/SCD_T_2005_0003_TSUKIOKA.pdf
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https://hal.univ-lorraine.fr/tel-01746707
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Submitted on : Thursday, March 29, 2018 - 10:43:03 AM
Last modification on : Tuesday, March 2, 2021 - 5:12:06 PM

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Toru Tsukioka. Sur les variétés de Fano obtenues par éclatement d'une courbe lisse dans une variété projective. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2005. Français. ⟨NNT : 2005NAN10003⟩. ⟨tel-01746707⟩

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