We study the blowing up of a smooth projective variety along a smooth center that is equipped with a projective bundle structure over a variety . If is a point, then is a projective space. If the Picard number is then has a lower bound Moreover, when is is a projective space and is a linear subspace in If is a projective space and is a curve, then either is and is a twisted cubic curve or is an arbitrary integer and is a line in . If is a quadric and is a curve, then is and is a line in .
Nous étudions l’éclatement d’une variété projective lisse le long d’un centre lisse , munie d’une structure de fbré projectif. Si est un point, est un espace projectif. Si le nombre de Picard est , alors a une borne inférieure . De plus, lorsque est , est un espace projectif et est un sous-espace linéaire dans . Si est l’espace projectif et B est une courbe, ou est égale à et est une courbe cubique tordue, ou est un entier arbitraire et est une ligne droite dans . Si est une quadrique et est une courbe, alors est égale à et est une ligne droite dans
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Duo Li 1
@article{CRMATH_2021__359_9_1129_0, author = {Duo Li}, title = {Projective bundles and blowing ups}, journal = {Comptes Rendus. Math\'ematique}, pages = {1129--1133}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {9}, year = {2021}, doi = {10.5802/crmath.249}, language = {en}, }
Duo Li. Projective bundles and blowing ups. Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1129-1133. doi : 10.5802/crmath.249. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.249/
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