Tokyo Journal of Mathematics

Isomorphism among Families of Weighted $K3$ Hypersurfaces

Masanori KOBAYASHI and Makiko MASE

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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

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

First available in Project Euclid: 23 January 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14J28: $K3$ surfaces and Enriques surfaces
Secondary: 14J10: Families, moduli, classification: algebraic theory 14J17: Singularities [See also 14B05, 14E15]


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.

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