## Tokyo Journal of Mathematics

### Isomorphism among Families of Weighted $K3$ Hypersurfaces

#### Abstract

It is known that there are exactly 95 weighted projective spaces having Gorenstein $K3$ surfaces as anticanonical divisors, some of which have isometric Picard lattices for generic members. For each set of such families, an explicit birational correspondence coming from a torus action is constructed in this paper. As a result the number of `essentially different' families of weighted Gorenstein $K3$ surfaces is 75.

#### Article information

Source
Tokyo J. Math., Volume 35, Number 2 (2012), 461-467.

Dates
First available in Project Euclid: 23 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1358951330

Digital Object Identifier
doi:10.3836/tjm/1358951330

Mathematical Reviews number (MathSciNet)
MR3058718

Zentralblatt MATH identifier
1262.14046

#### Citation

KOBAYASHI, Masanori; MASE, Makiko. Isomorphism among Families of Weighted $K3$ Hypersurfaces. Tokyo J. Math. 35 (2012), no. 2, 461--467. doi:10.3836/tjm/1358951330. https://projecteuclid.org/euclid.tjm/1358951330

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