Special birational transformations of projective spaces

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• 作者：Alberto Alzati^a ; ¹ ; ^{alberto.alzati@unimi.it" class="auth_mail" title="E-mail the corresponding author} ; José ; Carlos Sierra^b ; ² ; ^{jcsierra@icmat.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 14E05 ; secondary ; 14N05
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：5 February 2016
• 年：2016
• 卷：289
• 期：Complete
• 页码：567-602
• 全文大小：693 K

文摘

Extending some results of Crauder and Katz, and Ein and Shepherd-Barron on special Cremona transformations, we study birational transformations of P^r${\mathbb{P}}^r$ onto a prime Fano manifold such that the base locus X⊂P^r$X\subset {\mathbb{P}}^r$ is smooth irreducible and reduced. The main results are a complete classification when X has either dimension 1 and 2, or codimension 2. Partial results are also obtained when X has dimension 3.