Volume 11, issue 1 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 6, 2533–3057
Issue 5, 2007–2532
Issue 4, 1497–2006
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
The Meyer functions for projective varieties and their application to local signatures for fibered $4$–manifolds

Yusuke Kuno

Algebraic & Geometric Topology 11 (2011) 145–195
Bibliography
1 T Ashikaga, Normal two-dimensional hypersurface triple points and the Horikawa type resolution, Tohoku Math. J. $(2)$ 44 (1992) 177 MR1161610
2 T Ashikaga, K Konno, Global and local properties of pencils of algebraic curves, from: "Algebraic geometry 2000, Azumino (Hotaka)" (editors S Usui, M Green, L Illusie, K Kato, E Looijenga, S Mukai, S Saito), Adv. Stud. Pure Math. 36, Math. Soc. Japan (2002) 1 MR1971511
3 T Ashikaga, K I Yoshikawa, A divisor on the moduli space of curves associated to the signature of fibered surfaces (with an appendix by Kazuhiro Konno [2604074]), from: "Singularities—Niigata–Toyama 2007" (editors J P Brasselet, S Ishii, T Suwa, M Vaquie), Adv. Stud. Pure Math. 56, Math. Soc. Japan (2009) 1 MR2604073
4 M Atiyah, The logarithm of the Dedekind $\eta$–function, Math. Ann. 278 (1987) 335 MR909232
5 W P Barth, K Hulek, C A M Peters, A Van de Ven, Compact complex surfaces, Ergebnisse der Math. und ihrer Grenzgebiete. 3. Folge. 4, Springer (2004) MR2030225
6 J A Carlson, D Toledo, Discriminant complements and kernels of monodromy representations, Duke Math. J. 97 (1999) 621 MR1682991
7 I Dolgachev, A Libgober, On the fundamental group of the complement to a discriminant variety, from: "Algebraic geometry (Chicago, Ill., 1980)" (editors A Libgober, P Wagreich), Lecture Notes in Math. 862, Springer (1981) 1 MR644816
8 H Endo, Meyer's signature cocycle and hyperelliptic fibrations, Math. Ann. 316 (2000) 237 MR1741270
9 I M Gel’fand, M M Kapranov, A V Zelevinsky, Discriminants, resultants, and multidimensional determinants, Math.: Theory & Appl., Birkhäuser (1994) MR1264417
10 P Griffiths, J Harris, Principles of algebraic geometry, Wiley Classics Library, Wiley (1994) MR1288523
11 M Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. (1982) MR686042
12 J Harer, The second homology group of the mapping class group of an orientable surface, Invent. Math. 72 (1983) 221 MR700769
13 E Horikawa, On deformations of quintic surfaces, Proc. Japan Acad. 49 (1973) 377 MR0330173
14 S Iida, Adiabatic limits of $\eta$–invariants and the Meyer functions, Math. Ann. 346 (2010) 669 MR2578566
15 N Katz, Pinceaux de Lefschetz: théoréme d'existence, from: "Groupes de monodromie en géométrie algébrique. II", Lecture Notes in Math. 340, Springer (1973) 212 MR0354657
16 Y Kuno, The mapping class group and the Meyer function for plane curves, Math. Ann. 342 (2008) 923 MR2443768
17 K Lamotke, The topology of complex projective varieties after S Lefschetz, Topology 20 (1981) 15 MR592569
18 Y Matsumoto, On $4$–manifolds fibered by tori, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982) 298 MR682687
19 Y Matsumoto, Lefschetz fibrations of genus two—a topological approach, from: "Topology and Teichmüller spaces (Katinkulta, 1995)" (editors S Kojima, Y Matsumoto, K Saito, M Seppälä), World Sci. Publ. (1996) 123 MR1659687
20 W Meyer, Die Signatur von Flächenbündeln, Math. Ann. 201 (1973) 239 MR0331382
21 E Y Miller, The homology of the mapping class group, J. Differential Geom. 24 (1986) 1 MR857372
22 T Morifuji, On Meyer's function of hyperelliptic mapping class groups, J. Math. Soc. Japan 55 (2003) 117 MR1939188
23 S Morita, Characteristic classes of surface bundles, Invent. Math. 90 (1987) 551 MR914849
24 D Mumford, Algebraic geometry. I. Complex projective varieties, Grund. der Math. Wissenschaften 221, Springer (1976) MR0453732
25 D Mumford, Towards an enumerative geometry of the moduli space of curves, from: "Arithmetic and geometry, Vol. II" (editors M Artin, J Tate), Progr. Math. 36, Birkhäuser (1983) 271 MR717614
26 I Shimada, Generalized Zariski–van Kampen theorem and its application to Grassmannian dual varieties, Internat. J. Math. 21 (2010) 591 MR2650851
27 V G Turaev, First symplectic Chern class and Maslov indices, J. Soviet Math. 37 (1987) 1115 MR806563