Taiwanese Journal of Mathematics

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

Keiji Oguiso

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Abstract

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

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

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874613

Digital Object Identifier
doi:10.11650/tjm/7833

Mathematical Reviews number (MathSciNet)
MR3661387

Zentralblatt MATH identifier
06871338

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

Keywords
quartic K3 surfaces Cremona equivalence projective equivalence

Citation

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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