Luigi Cremona and cubic surfaces
英文摘要:
We discuss Luigi Cremona's contribution to the early development of the theory of cubic surfaces.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
Igor V. Dolgachev
We discuss Luigi Cremona's contribution to the early development of the theory of cubic surfaces.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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We give a fine classification of cubic plane Cremona maps. A previous partial classification was obtained by Cerveau and Déserti a few years ago.
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A famous result of B. Crauder and S. Katz (1989) concerns the classification of special Cremona transformations whose base locus has dimension at most two. Furthermore, they also proved that a special Cremona transformation with base locus of dimension three has to be one of the following: 1) a quinto-quintic transformation of $\mathbb{P}^5$; 2) a cubo-quintic transformation of $\mathbb{P}^6$; or 3) a quadro-quintic transformation of $\mathbb{P}^8$. Special Cremona transformations as in case 1) have been classified by L. Ein and N. Shepherd-Barron (1989), while in our previous work (2013), we …
In this note we observe that the Cremona transformation in Oguiso's example of Cremona isomorphic but not projectively equivalent quartic K3 surfaces in three-dimensional projective space is the classical cubo-cubic transformation.
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本文确定了所有有限域上秩 2 的 Cremona 群的 Jordan 常数精确值,并构造了 $\mathbb{F}_2$ 上具有最大自同构群 $\mathrm{S}_6$ 的正则作用的三次曲面,且证明了其唯一性。
We give a method for constructing many examples of automorphisms with positive entropy on rational complex surfaces. The general idea is to begin with a quadratic Cremona transformation that fixes a reduced cubic curve and then use the group structure on the cubic to understand when the indeterminacy and exceptional behavior of the transformation may be eliminated by repeated blowing up.
A Pascal-type construction of the Segre cubic and the Cremona--Richmond configuration
本文提出P^4中的Pascal型剩余构造,从两对超平面出发,证明十二个剩余平面位于一个三次三维流形上,一般情况为Segre三次曲面,并恢复其十五个平面和关联的Cremona–Richmond构型,同时给出该构型的点线实现。
For any $n\geq 3$, we prove that there exist equivalences between these apparently unrelated objects: irreducible $n$-dimensional non degenerate projective varieties $X\subset \mathbb P^{2n+1}$ different from rational normal scrolls and 3-covered by twisted cubic curves, up to projective equivalence; quadro-quadric Cremona transformations of $ \mathbb P^{n-1}$, up to linear equivalence; $n$-dimensional complex Jordan algebras of rank three, up to isotopy. We also provide some applications to the classification of particular classes of varieties in the class defined above and of quadro-quadric …
We extend our classification of special Cremona transformations whose base locus has dimension at most three to the case when the target space is replaced by a (locally) factorial complete intersection.
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