[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2008.45.2.221

A CHARACTERIZATION OF THE VANISHING OF THE SECOND PLURIGENUS FOR NORMAL SURFACE SINGULARITIES

Wada, Koukichi (The Second High School Tokyo University of Agriculture)

Publication Information

Bulletin of the Korean Mathematical Society / v.45, no.2, 2008 , pp. 221-230 More about this Journal

Abstract

In the study of normal (complex analytic) surface singularities, it is interesting to investigate the invariants. The purpose of this paper is to give a characterization of the vanishing of ${\delta}_2$ . In [11], we gave characterizations of minimally elliptic singularities and rational triple points in terms of th.. second plurigenera ${\delta}_2$ and ${\gamma}_2$ . In this paper, we also give a characterization of rational triple points in terms of a certain computation sequence. To prove our main theorems, we give two formulae for ${\delta}_2$ and ${\gamma}_2$ of rational surface singularities.

Keywords

second plurigenus; rational surface singularity; rational triple points;

Citations & Related Records

Times Cited By Web Of Science : 0 (Related Records In Web of Science)
Times Cited By SCOPUS : 0

Reference

1	J. Lipman, Rational singularities, with applications to algebraic surfaces and unique factorization, Inst. Hautes Etudes Sci. Publ. Math. 36 (1969), 195-279 DOI
2	G. N. Tjurina, Absolute isolation of rational singularities, and triple rational points, Functional Anal. i Prilozen. 2 (1968), no. 4, 70-81
3	K. Wada, The behavior of the second pluri-genus of normal surface singularities of type $_A_n,\;_D_n,\;_E_n,\;_\tilde{A}_n,\;_D_n\;and\;_\tilde{E}_n$ , Math. J. Okayama. Univ. 45 (2003), 45-58
4	K. Wada, Characterizations of minimally elliptic singularities and rational triple points, Saitama Math. J. 22 (2004), 1-9
5	K. Wada, On some properties of the second plurigenera of normal surface singularities, Thesis, University of Tsukuba, 2005
6	K. Watanabe, On plurigenera of normal isolated singularities. I, Math. Ann. 250 (1980), 65-94 DOI
7	M. Artin, On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966), 129-136 DOI ScienceOn
8	F. W. Knoller, 2-dimensionale Singularitaten und Differentialformen, Math. Ann. 206 (1973), 205-213 DOI
9	H. B. Laufer, On rational singularities, Amer. J. Math. 94 (1972), 597-608 DOI ScienceOn
10	H. B. Laufer, On minimally elliptic singularities, Amer. J. Math. 99 (1977), no. 6, 1257-1295 DOI ScienceOn
11	T. Okuma, The pluri-genera of surface singularities, Tohoku Math. J. (2) 50 (1998), no. 1, 119-132 DOI
12	T. Okuma, The second pluri-genus of surface singularities, Compositio Math. 110 (1998), no. 3, 263-276 DOI ScienceOn
13	T. Okuma, The polynomial periodicity of the plurigenera of surface singularities, Saitama Math. J. 17 (1999), 7-13