Quartic surfaces of elliptic ruled type

Umezu, Yumiko

doi:10.1090/S0002-9947-1984-0735411-3

Quartic surfaces of elliptic ruled type
HTML articles powered by AMS MathViewer

by Yumiko Umezu

Trans. Amer. Math. Soc. 283 (1984), 127-143

DOI: https://doi.org/10.1090/S0002-9947-1984-0735411-3

PDF | Request permission

Abstract:

Let $X$ be a normal quartic surface whose resolutions are birationally equivalent to elliptic ruled surfaces. We classify the singularities on $X$ and then describe the global structure of $X$.

References

Fumio Hidaka and Keiichi Watanabe, Normal Gorenstein surfaces with ample anti-canonical divisor, Tokyo J. Math. 4 (1981), no. 2, 319–330. MR 646042, DOI 10.3836/tjm/1270215157
Henry B. Laufer, On minimally elliptic singularities, Amer. J. Math. 99 (1977), no. 6, 1257–1295. MR 568898, DOI 10.2307/2374025
Yumiko Umezu, On normal projective surfaces with trivial dualizing sheaf, Tokyo J. Math. 4 (1981), no. 2, 343–354. MR 646044, DOI 10.3836/tjm/1270215159
Stephen Shing Toung Yau, On maximally elliptic singularities, Trans. Amer. Math. Soc. 257 (1980), no. 2, 269–329. MR 552260, DOI 10.1090/S0002-9947-1980-0552260-6
Stephen Shing Toung Yau, Hypersurface weighted dual graphs of normal singularities of surfaces, Amer. J. Math. 101 (1979), no. 4, 761–812. MR 536041, DOI 10.2307/2373918
Stephen Shing Toung Yau, Gorenstein singularities with geometric genus equal to two, Amer. J. Math. 101 (1979), no. 4, 813–854. MR 536042, DOI 10.2307/2373919