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On the cylinder homomorphisms of Fano complete intersections
Ichiro SHIMADA
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Ichiro SHIMADA
Department of Mathematics Faculty of Science University of Tokyo
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1990 Volume 42 Issue 4 Pages 719-738
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- Published: 1990 Received: April 19, 1989 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) W. Barth and A. Van de Ven, Fano varieties of lines on hypersurf aces, Arch. Math., 31 (1978), 94-104.
2) A. Beauville, Variétés de Prym et jacobiennes intermédiaires, Ann. Sci. École Norm. Sup., 10 (1977), 309-391.
3) A. Beauville and R. Donagi, La variété des droites d'une hypersurface cubique de dimension 4, C.R. Acad. Sci. Paris, 301 (1985), 703-706.
4) G. Ceresa and A. Verra, The Abel-Jacobi isomorphism for the sextic double solid, Pacific J. Math., 124 (1986), 85-105.
5) H. Clemens, The local geometry of the Abel-Jacobi mapping, AMS Proc. Symp. Pure Math., 46 (1987), 223-233.
6) C. H. Clemens and P. A. Griffiths, The intermediate Jacobian of the cubic threefold, Ann. of Math., 95 (1972), 281-356.
7) A. Collino, The Abel-Jacobi isomorphism for the cubic fivefold, Pacific J. Math., 122 (1986), 43-55.
8) A. Collino, J. P. Murre and G. E. Welters, On the family of conics lying on a quartic threefold, Rend. Sem. Mat. Univ. Politec. Torino, 38 (1980), 151-181.
9) A. Conte and J. P. Murre, The Hodge conjecture for Fano complete intersections of dimension four, Journées de géométrie algébrique d'Angers (juillet 1979), Sijthoff & Noordhoff, 1980, pp. 129-141.
10) P. A. Griffiths, Periods of integrals on algebraic manifolds, II, (Local study of the period mapping), Amer. J. Math., 90 (1968), 805-865.
11) K. Lamotke, The topology of complex projective varieties after S. Lefschetz, Topology, 20 (1981), 15-51.
12) M. Letizia, The Abel-Jacobi mapping for the quartic threefold, Invent. Math., 75 (1984), 477-492.
13) J. D. Lewis, The Hodge conjecture for a certain class of fourfolds, Math. Ann., 268 (1984), 85-90.
14) J. D. Lewis, The cylinder homomorphism associated to quintic fourfolds, Compositio Math., 56 (1985), 315-329.
15) J. D. Lewis, The cylinder correspondence for hypersurfaces of degree a in Pn, Amer. J. Math., 110 (1988), 77-114.
16) J. Milnor, Morse theory, Ann. of Math. Stud., 51, Princeton, 1963.
17) I. Shimada, On the cylinder isomorphism associated to the family of lines on a hypersurface, preprint.
18) T. Shioda, Algebraic cycles on hypersurfaces in PN, Adv. Stud. Pure Math., 10, Kinokuniya and North-Holland, 1987, pp. 717-732.
19) B. R. Tennison, On the quartic threefold, Proc. London Math. Soc., 29 (1974), 714-734.
20) A. S. Tihomirov, The intermediate Jacobian of the double covering of P3 branched at a quartic, Math. USSR-Izv., 17 (1981), 523-566.
21) A. N. Tyurin, Five lectures on three-dimensional varieties, Russian Math. Surveys, 27 (1972), 1-53.
22) G. E. Welters, Abel-Jacobi isogenies for certain types of Fano threefolds, Mathematisch Centrum, Amsterdam, 1981.
23) SGA 7II, Groupes de Monodromie en Géomérie Algébrique, Lecture Notes in Math., 340, Springer, 1973.
Right : [1] W. Barth and A. Van de Ven, Fano varieties of lines on hypersurfaces, Arch. Math., 31 (1978), 94-104.
[2] A. Beauville, Variétés de Prym et jacobiennes intermédiaires, Ann. Sci. École Norm. Sup., 10 (1977), 309-391.
[3] A. Beauville and R. Donagi, La variété des droites d'une hypersurface cubique de dimension 4, C. R. Acad. Sci. Paris, 301 (1985), 703-706.
[4] G. Ceresa and A. Verra, The Abel-Jacobi isomorphism for the sextic double solid, Pacific J. Math., 124 (1986), 85-105.
[5] H. Clemens, The local geometry of the Abel-Jacobi mapping, AMS Proc. Symp. Pure Math., 46 (1987), 223-233.
[6] C. H. Clemens and P. A. Griffiths, The intermediate Jacobian of the cubic threefold, Ann. of Math., 95 (1972), 281-356.
[7] A. Collino, The Abel-Jacobi isomorphism for the cubic fivefold, Pacific J. Math., 122 (1986), 43-55.
[8] A. Collino, J. P. Murre and G. E. Welters, On the family of conics lying on a quartic threefold, Rend. Sem. Mat. Univ. Politec. Torino, 38 (1980), 151-181.
[9] A. Conte and J. P. Murre, The Hodge conjecture for Fano complete intersections of dimension four, Journées de géométrie algébrique d'Angers (juillet 1979), Sijthoff & Noordhoff, 1980, pp. 129-141.
[10] P. A. Griffiths, Periods of integrals on algebraic manifolds, II, (Local study of the period mapping), Amer. J. Math., 90 (1968), 805-865.
[11] K. Lamotke, The topology of complex projective varieties after S. Lefschetz, Topology, 20 (1981), 15-51.
[12] M. Letizia, The Abel-Jacobi mapping for the quartic threefold, Invent. Math., 75 (1984), 477-492.
[13] J. D. Lewis, The Hodge conjecture for a certain class of fourfolds, Math. Ann., 268 (1984), 85-90.
[14] J. D. Lewis, The cylinder homomorphism associated to quintic fourfolds, Compositio Math., 56 (1985), 315-329.
[15] J. D. Lewis, The cylinder correspondence for hypersurfaces of degree n in Pn, Amer. J. Math., 110 (1988), 77-114.
[16] J. Milnor, Morse theory, Ann. of Math. Stud., 51, Princeton, 1963.
[17] I. Shimada, On the cylinder isomorphism associated to the family of lines on a hypersurface, preprint.
[18] T. Shioda, Algebraic cycles on hypersurfaces in PN, Adv. Stud. Pure Math., 10, Kinokuniya and North-Holland, 1987, pp. 717-732.
[19] B. R. Tennison, On the quartic threefold, Proc. London Math. Soc., 29 (1974), 714-734.
[20] A. S. Tihomirov, The intermediate Jacobian of the double covering of P3 branched at a quartic, Math. USSR-Izv., 17 (1981), 523-566.
[21] A. N. Tyurin, Five lectures on three-dimensional varieties, Russian Math. Surveys, 27 (1972), 1-53.
[22] G. E. Welters, Abel-Jacobi isogenies for certain types of Fano threefolds, Mathematisch Centrum, Amsterdam, 1981.
[23] SGA 7II, Groupes de Monodromie en Géométrie Algébrique, Lecture Notes in Math., 340, Springer, 1973.
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