## Taiwanese Journal of Mathematics

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

Keiji Oguiso

#### 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

https://projecteuclid.org/euclid.twjm/1498874613

Digital Object Identifier
doi:10.11650/tjm/7833

Mathematical Reviews number (MathSciNet)
MR3661387

Zentralblatt MATH identifier
06871338

#### 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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