Kodai Mathematical Journal

$(2,3)$ torus sextics and the Albanese images of $6$-fold cyclic multiple planes

Hiro-o Tokunaga

Full-text: Open access

Article information

Source
Kodai Math. J., Volume 22, Number 2 (1999), 222-242.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1138044044

Digital Object Identifier
doi:10.2996/kmj/1138044044

Mathematical Reviews number (MathSciNet)
MR1700594

Zentralblatt MATH identifier
0990.14010

Subjects
Primary: 14H50: Plane and space curves
Secondary: 14E20: Coverings [See also 14H30]

Citation

Tokunaga, Hiro-o. $(2,3)$ torus sextics and the Albanese images of $6$-fold cyclic multiple planes. Kodai Math. J. 22 (1999), no. 2, 222--242. doi:10.2996/kmj/1138044044. https://projecteuclid.org/euclid.kmj/1138044044


Export citation

References

  • [A] E. ARTAL BARTOLO, Sur les couples de Zaski, J. Algebraic Geom., 3 (1994), 223-247
  • [Bl] E. BRIESKORN, Uber die Auflsung gewisser Singulataten von holomorpher Abbildun gen, Math. Ann., 166 (1966), 76-102.
  • [B2] E. BRIESKORN, Die Auflsung der rationalen Singurantaten holomoher Abbildungen, Math. Ann., 178 (1968), 255-270
  • [BdF] G. BAGNERA AND M. DE FRANCHIS, Le superficie algebche le quali ammettono un rappresentazione parametca mediante funzioni iperellittiche de due argomenti, Mem. Accad. dei XL, 15 (1908), 251-343.
  • [Ca] F. CATANESE, On the moduli spaces of surfaces of general type, J. Differential Geom. 1 (1984), 483-515.
  • [CC] F. CATANESE AND C. CILIBERTO, On the irregularity of cyclic covering of algebraic surfaces, Geometry of Complex Projective Varieties, Sem. Conf., 9, Mediterranean Press, Rende, 1993, 89-115
  • [Co] A. COMMESSATTI, Sui piam tpli ciclici irregolari, Rend. Circ. Mat. Palermo, 31 (1911), 293-310
  • [CP] D. Cox AND W PARRY, Torsion in elliptic curves over kit), Compositio Math., 41 (1980), 337-354
  • [D] A. DEGTYAREV, Alexander polynomial of a curve of degree six, J. Knot Theory Ram ifications, 3 (1994), 439-454.
  • [DF1] M. DE FRANCHIS, I piam doppi dotati di due o piu differenziali totali di pma specie, Rend. Accad. Lincei, 13 (1904), 688-695
  • [DF2] M. DEFRANCHIS, Sugli integrali di Picard relativi ad una superficie doppia, Rend. Circ Palermo, 20 (1905), 331-334.
  • [H] E. HORIKAWA, On deformation of quintic surfaces, Invent. Math., 31 (1975), 43-85
  • [1] J. -I. IGUSA, Fiber systems of Jacobian varieties (III), Amer. J. Math., 81 (1959), 453 476.
  • [Ku] VIK. S. KULIKOV, On plane algebraic curves of positive Albanese dimension, prepnt
  • [Ko] K. KODAIRA, On compact analytic surfaces II, III, Ann. of Math., 77 (1963), 563-626, 7 (1963), 1-40.
  • [L] A. LIBGOBER, Alexander polynomials of plane algebraic curves and cyclic multiple planes, Duke Math. J., 49 (1982), 833-851
  • [M] R. MIRANDA, The Basic Theory of Elliptic Surfaces, Dottorato Ric. Mat., ETS Editce, Pisa, 1989
  • [MP1] R. MIRANDA AND U. PERSSON, On extremal rational elliptic surfaces, Math. Z., 193 (1986), 537-558
  • [MP2] R. MIRANDA AND U. PERSSON, Configurations of /, , fibers on elliptic K3 surfaces, Math. Z., 201 (1989), 339-361
  • [MP3] R. MIRANDA AND U. PERSSON, Mordell-Weil groups of extremal elliptic K3 surfaces, 242HIRO-O TOKUNAG Problems in the Theory of Surfaces and their classification, Sympos. Math., 32, Academic Press, 1991, 167-192.
  • [PI] U. PERSSON, Horikawa surfaces with maximal Picard number, Math. Ann., 259 (1982), 287-312
  • [P2] U. PERSSON, Double sextics and singular K-3 surfaces, Algebraic Geometry Sitges 1983, Lecture Notes m Math., 1124, Sponger, 1985, 262-328
  • [SI] T. SHIODA, On elliptic modular surfaces, J. Math. Soc. Japan, 24 (1972), 29-59
  • [S2] T. SHIODA, On the Mordell-Weil lattices, Comment. Math. Univ. St. Paul., 39 (1990), 211 240.
  • [Sa] F. SAKAI, On the irregularity of cyclic coverings of the projective plane, Classification o Algebraic Vaeties, Contemp. Math., 162, Amer. Math. Soc, 1994, 359-369.
  • [Tl] H. TOKUNAGA, A remark on Artal's paper, Kodai Math. J., 19 (1996), 207-217
  • [T2] H. TOKUNAGA, Dihedral Galois coverings branched along maximizing sextics, Math. Ann., 308 (1997), 633-648
  • [T3] H. TOKUNAGA, Some examples of Zanski pairs arising from certain elliptic K3 surfaces, Math. Z, 227 (1998), 465-47
  • [T4] H. TOKUNAGA, Some examples of Zanski pairs asing from certain elliptic K3 surfaces II, to appear in Math. Z.
  • [T5] H. TOKUNAGA, Irreducible plane curves with the Albanese dimension 2, to appear in Proc Amer. Math. Soc.
  • [Y] J. -G. YANG, Sextic curves with simple singularities, Thoku Math. J., 48 (1996), 203-22
  • [Zl] O. ZARISKI, On the linear connection index of the algebraic surfaces zn --f(x, y), Proc Nat. Acad. Sci., 15 (1929), 494-501.
  • [Z2] O. ZARISKI, On the irregularity of cyclic multiple planes, Ann. of Math., 32 (1931) 485 511.