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Since 15 years ago, I have been studying some relations between complex normal surfaces (...). In this paper, we give a survey of them. After some preparations, we describe main results. Especially, we explain a method to embed resolution spaces of normal surface singularities into total spaces of degenerations of compact Riemann surfaces.
Słowa kluczowe
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Czasopismo
Rocznik
Tom
Strony
339--359
Opis fizyczny
Bibliogr. 34 poz.
Twórcy
autor
- School of Health Sciences Gunma University Maebashi, Gunma 371-8514 Japan, ttomaru@health.gunma-u.ac.jp
Bibliografia
- [1] V. I. Arnold, Normal forms of functions, Invent. Math. 35 (1976), 87–109.
- [2] M. Artin, On isolated rational singularities of surfaces, Amer. J. Math. 88 (1963), 129–138.
- [3] T. Ashikaga, Surface singularities on cyclic coverings and an inequality for the signature, J. Math. Soc. Japan 51 (1999), 485–521.
- [4] W. Barth, C. Peters, A. Van de Ven, Compact Complex Surfaces, Ergebnisse der Mathematik, Band 4, Springer-Verlag, 1984.
- [5] W. Ebeling, C. T. C. Wall, Kodaira singularities and an extension of Arnold’s strange duality, Compositio Math. 56 (1985), 3–77.
- [6] A. Fujiki, On isolated singularities with C*-action. Master thesis, Kyoto University (197), (in Japanese).
- [7] A. Fujiki, On resolution of cyclic quotient singularities, Publ. RIMS Kyoto Univ. 10 (1974), 293–328.
- [8] H. Grauert, Über Modifikationen und exceptionelle analytische Mengen, Math. Ann. 146 (1962), 311–368.
- [9] U. Karras, On pencils of curves and deformations of minimally elliptic singularities, Math. Ann. 247 (1980), 43–65.
- [10] U. Karras, Methoden zur Berechnung von Algebraischen Invarianten und zur Konstruktion von Deformationen Normaler Flachensingularitaten, Habilitationschrift, Dortmund 1981.
- [11] K. Kodaira, On compact analytic surface II, Ann. of Math. 77 (1963), 563–626.
- [12] V. S. Kulikov, Degenerate elliptic curves and resolution of uni- and bimodal singularities, Funct. Anal. Appl. 9 (1975), 69–70.
- [13] H. Laufer, On minimally elliptic singularities, Amer. J. Math. 99 (1977), 1257–1295.
- [14] E. Looijenga, Riemann-Roch and smoothing of singularities, Topology 25 (3) (1986), 293–302.
- [15] M. Namba, Geometry of Projective Algebraic Curves, Marcel Dekker, (1984).
- [16] Y. Namikawa, K. Ueno, The complete classification of fibres in pencils of curves of genus two, Manuscripta Math. 9 (1973), 143–186.
- [17] T. Okuma, Plurigenera of Surface Singularities, Nova Science Publishers, New York, 2000.
- [18] P. Orlik, P. Wagreich, Isolated singularities of algebraic surfaces with C*-action, Ann. Math. 93 (1971), 205–228.
- [19] H. Pinkham, Normal surface singularities with C*-action, Math. Ann. 227 (1977), 183–193.
- [20] M. Reid, Elliptic Gorenstein singularities of surfaces, Preprint (1978).
- [21] K. Saito, Algebraic surfaces for regular systems of weights, Algebraic Geometry, Commutative Algebra II - in honor of Masayoshi NAGATA (H. Hijikata et al., eds.), Kinokuniya, Tokyo, (1987), 517–614.
- [22] J. Stevens, Elliptic surface singularities and smoothings of curves, Math. Ann. 267 (1984), 239–249.
- [23] J. Stevens, Kulikov Singularities, Thesis, Leiden, 1985.
- [24] M. Tomari, A pg-formula and elliptic singularities, Publ. Res. Inst. Math. Sci. Kyoto Univ. 21 (2), (1985), 297–354.
- [25] M. Tomari, Maximal-ideal-adic filtration on (….) for normal two-dimensional singularities, Complex analytic singularities, Adv. Stud. Pure Math., North-Holland, Amsterdam, 8 (1987), 633–647.
- [26] M. Tomari, K-i. Watanabe, Cyclic covers of normal graded rings, Kodai Math. J. 24 (2001), 436–457.
- [27] T. Tomaru, On Gorenstein surface singularities with fundamental genus pf (…)2 which satisfy some minimality conditions, Pacific J. Math. 170 (1995), 271–295.
- [28] T. Tomaru, On Kodaira singularities defined by zn = f(x, y), Math. Z. 236 (2001), 133–149.
- [29] T. Tomaru, On some classes of weakly Kodaira singularities, Séminaires & Congrés, “Singularités Franco-Japonaises” 10 (2005), 323–340.
- [30] T. Tomaru, Pencil genus for normal surface singularities, J. Math. Soc. Japan 59 (1) (2007), 35–80.
- [31] T. Tomaru, Normal C*-surface singularities and C*-pencils of curves, (in preparation).
- [32] P. Wagreich, Elliptic singularities of surfaces, Amer. J. Math. 92 (1970), 421–454.
- [33] K-i. Watanabe, Some remarks concerning Demazure’s construction of normal graded rings, Nagoya Math. J. 83 (1981), 203–211.
- [34] S. S.-T. Yau, On maximally elliptic singularities, Trans. Amer. Math. Soc. 257 (2) (1980), 269–329.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0032-0003