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The signature of fibered complex surfaces is sometimes localized at finite fiber germs. We analyze this phenomenon by using datum of local monodromy in the mapping class group and a certain rational divisor on the moduli space of stable curves.
Wydawca
Czasopismo
Rocznik
Tom
Strony
263--276
Opis fizyczny
Bibliogr. 37 poz.
Twórcy
autor
- Faculty of Engineering Tohoku-Gakuin University, Tagajo, Miyagi, 985-8537, Japan, tashikaga@tjcc.tohoku-gakuin.ac.jp
Bibliografia
- [1] T. Arakawa, T. Ashikaga, Local splitting families of hyperelliptic pencils, I: Tohoku Math. J. 53 (2001), 369–394. II: Nagoya Math. J. 175 (2004), 103–124.
- [2] T. Ashikaga, Local signature defect of fibered complex surfaces via monodromy and stable reduction, Comment. Math. Helv. 85 (2010), 417–461.
- [3] T. Ashikaga, H. Endo, Various aspects of degenerate families of Riemann surfaces, Sugaku Exposition 19 (2006), Amer. Math. Soc., 171–196.
- [4] T. Ashikaga, M. Ishizaka, A geometric proof of the reciprocity law of Dedekind sum, Preprint (2009).
- [5] T. Ashikaga, K. Konno, Global and local properties of pencils of algebraic curves, in Algebraic Geometry 2000 Azumino, ed. by S. Usui et al., Adv. Stud. Pure Math. 36 (2002), 1–49.
- [6] T. Ashikaga, K. Yoshikawa, A divisor on the moduli space of curves associated to the signature of fibered surfaces (with an appendix by K. Konno), Adv. Stud. Pure Math. 56, Math. Soc. Japan, Tokyo 2009, 1–34.
- [7] M. Atiyah, The logarithm of Dedekind ŋ-function, Math. Ann. 278 (1987), 335–380.
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- [9] Z. Chen, S. L. Tan, Upper bound on the slope of a genus 3 fibration, Preprint, (2005).
- [10] P. Deligne, D. Mumford, The irreducibility of the space of curves of given genus, Publ. Math. I.H.E.S. 36 (1969), 75–110.
- [11] H. Endo, Meyer’s signature cocycle and hyperelliptic fibrations (with Appendix written by T. Terasoma), Math. Ann. 316 (2000), 237–257.
- [12] M. Furuta, Surface bundle and local signature, in; The report of the symposium of Topology related to Riemann surfaces, ed. by N. Kawazumi, pp. 47–53, 1999, in Japanese.
- [13] M. Furuta, Surface bundle and local signature, in; The report of the symposium of Algebraic Geometry at Kinosaki, pp. 94–103, 2000, in Japanese.
- [14] J. Harris, D. Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982), 23–86.
- [15] J. Harris, I. Morrison, Moduli of Curves, Springer, Berlin, (1998).
- [16] E. Horikawa, On algebraic surfaces with pencils of curves of genus 2, In Complex Analysis and Algebraic Geometry, a volume dedicated to K. Kodaira, Iwanami Shoten Publishers and Cambridge University Press, Tokyo and Cambridge, (1977), 79–90.
- [17] S. Iida, Adiabatic limits of ŋ-invariants and the Meyer functions, Math. Ann. 346 (2010), 669–717.
- [18] Y. Imayoshi, Holomorphic families of Riemann surfaces and Teichmüller spaces, In Riemann surfaces and related topics, Ann. of Math. Stud. 97, Princeton Univ. Press, (1981), 277–300.
- [19] K. Konno, Clifford index and the slope of fibered surfaces, J. Algebraic Geom. 8 (1999), 207–220.
- [20] K. Konno, An appendix to the paper of Ashikaga and Yoshikawa [6], Preprint (2008).
- [21] Y. Kuno, The mapping class group and the Meyer function for plane curves, Math. Ann. 342 (2008), 923–949.
- [22] Y. Matsumoto, J. M. Montesinos-Amilibia, Pseudo-periodic maps and degeneration of Riemann surfaces, I, II, Preprints, Univ. of Tokyo and Univ. Complutense de Madrid, 1991/1994 (Revised in 2006).
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- [24] Y. Matsumoto, On 4-manifolds fibered by tori, I, Proc. Japan Acad. 58 (1982), 298–301; II, ibid. 59 (1983), 100–103.
- [25] Y. Matsumoto, Lefschetz fibrations of genus two — a topological approach, in Proceedings of the 37th Taniguchi Symposium on “Topology and Teichmüller Spaces”, World Scientific, Singapore, (1996), 123–148.
- [26] T.Morifuji, On Meyer’s function of hyperelliptic mapping class groups, J. Math. Soc. Japan 55 (2003), 117–129.
- [27] J. Nielsen, Die Structur periodischer Transformation von Flächen, Mat. -Fys. Medd. Danske Vid. Selsk. 15 (1937). English translation : in Collected Papers 2, Birkhäuser, 1986.
- [28] J. Nielsen, Surface transformation classes of algebraically finite type, Mat.-Fys.Medd. Danske Vid. Selsk. 21 (1944), 3–89. English translation; in Collected Papers 2, Birkhäuser, 1986.
- [29] S. Ogata, M. Saito, Signature defect and eta functions of degenerations of Abelian varieties, Japan. J. Math. 23, 319–364.
- [30] M. Reid, Problems on pencils of small genus, Preprint (in his home page), (1990).
- [31] M. Sato, Local signature for fibrations with a finite group action, Preprint (arXiv: 0912.1952v1 [math.GT]10Dec2009).
- [32] I. Smith, Lefschetz fibrations and the Hodge bundle, Geometry and Topology 3 (1999), 211–233.
- [33] S. Takamura, Towards the classification of atoms of degenerations II, (Cyclic quotient construction of degenerations of complex curves), RIMS Preprint 1344 (2001).
- [34] S. L. Tan, On the invariants of base changes of pencils of curves, I: Manuscripta Math. 84 (1994), 225–244. II: Math. Z. 222 (1996), 655–676.
- [35] K. Ueno, Discriminants of curves of genus 2 and arithmetic surfaces, in Algebraic Geometry and Commutative Algebra in honor of M. Nagata, Kinokuniya, Tokyo, (1987), 749–770.
- [36] G. Xiao, The fibrations of algebraic surfaces, Shanghai Scientific and Technical Publishers, (1992), in Chinese.
- [37] K. Yoshikawa, A local signature for generic 1-parameter deformation germs of a complexcurve, in The report on the symposium on Algebraic Geometry and Topology of Degenerations, Coverings and Singularities (2000), 188–200, in Japanese.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0027-0041