Birational rigidity of complete intersections

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• 作者：Fumiaki Suzuki
• 关键词：Birational rigidity ; Complete intersections ; Rationality problem
• 刊名：Mathematische Zeitschrift
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：285
• 期：1-2
• 页码：479-492
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1823
• 卷排序：285

文摘

We prove that every smooth complete intersection \(X=X_{d_{1}, \ldots , d_{s}}\subset \mathbb {P}^{\sum _{i=1}^{s}d_{i}}\) defined by s hypersurfaces of degree \(d_{1}, \ldots , d_{s}\) is birationally superrigid if \(5s +1\le \frac{2(\sum _{i=1}^{s}d_{i}+1)}{\sqrt{\prod _{i=1}^{s}d_{i}}}\). In particular, X is non-rational and \({{\mathrm{Bir}}}(X)={{\mathrm{Aut}}}(X)\). We also prove birational superrigidity of singular complete intersections with similar numerical condition. These extend the results proved by Tommaso de Fernex.