Taiwanese Journal of Mathematics

Isomorphic Quartic K3 Surfaces in the View of Cremona and Projective Transformations

Keiji Oguiso

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We show that there is a pair of smooth complex quartic K3 surfaces $S_1$ and $S_2$ in $\mathbb{P}^3$ such that $S_1$ and $S_2$ are isomorphic as abstract varieties but not Cremona isomorphic. We also show, in a geometrically explicit way, that there is a pair of smooth complex quartic K3 surfaces $S_1$ and $S_2$ in $\mathbb{P}^3$ such that $S_1$ and $S_2$ are Cremona isomorphic, but not projectively isomorphic. This work is much motivated by several e-mails from Professors Tuyen Truong and János Kollár.

Article information

Taiwanese J. Math., Volume 21, Number 3 (2017), 671-688.

First available in Project Euclid: 1 July 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14J28: $K3$ surfaces and Enriques surfaces 14J50: Automorphisms of surfaces and higher-dimensional varieties

quartic K3 surfaces Cremona equivalence projective equivalence


Oguiso, Keiji. Isomorphic Quartic K3 Surfaces in the View of Cremona and Projective Transformations. Taiwanese J. Math. 21 (2017), no. 3, 671--688. doi:10.11650/tjm/7833. https://projecteuclid.org/euclid.twjm/1498874613

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