Intersection numbers for normal functions
Author:
C. Herbert Clemens
Journal:
J. Algebraic Geom. 22 (2013), 565-573
DOI:
https://doi.org/10.1090/S1056-3911-2012-00582-7
Published electronically:
December 19, 2012
MathSciNet review:
3048545
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Abstract |
References |
Additional Information
Abstract: The purpose of this note is to simplify and generalize a formula of M. Green and P. Griffiths for the intersection number of two normal functions in complex algebraic geometry.
References
- C. H. Clemens, Degeneration of Kähler manifolds, Duke Math. J. 44 (1977), no. 2, 215–290. MR 444662
- P. Deligne, Théorème de Lefschetz et critères de dégénérescence de suites spectrales, Inst. Hautes Études Sci. Publ. Math. 35 (1968), 259–278 (French). MR 244265
- Mark Green and Phillip Griffiths, Algebraic cycles and singularities of normal functions, Algebraic cycles and motives. Vol. 1, London Math. Soc. Lecture Note Ser., vol. 343, Cambridge Univ. Press, Cambridge, 2007, pp. 206–263. MR 2385303, DOI https://doi.org/10.1017/CBO9780511721496.006
- Gerard van der Geer and Alexis Kouvidakis, The rank-one limit of the Fourier-Mukai transform, Doc. Math. 15 (2010), 747–763. MR 2735987
- Christian Schnell, Complex analytic Néron models for arbitrary families of intermediate Jacobians, Invent. Math. 188 (2012), no. 1, 1–81. MR 2897692, DOI https://doi.org/10.1007/s00222-011-0341-8
References
- Clemens, H. “Degeneration of Kähler manifolds.” Duke Math. Journal 44(1977), 215-290. MR 0444662 (56:3012)
- Deligne, P. “Théorème de Lefschetz et Critères de Dégénéresence de Suites Spectrales.” Publ. Math. IHES 35(1968), 259-278. MR 0244265 (39:5582)
- Green, M., Griffiths, P. “Algebraic cycles and singularities of normal functions.” EAGER Conf. on Algebraic Cycles and Motives in honor of J. Murre, 30 August–3 September, 2004. Cambridge Univ. Press (2007), 220-278. MR 2385303 (2009b:14013)
- van der Geer, G., Kouvidakis, A. “The rank-one limit of the Fourier-Mukai transform.” Documenta Mathematica 15 (2010), 747–763. MR 2735987 (2012a:14015)
- Schnell, C. “Complex analytic Néron models for arbitrary families of intermediate Jacobians.” Inventiones Math. 188 (2012), 1–81. MR 2897692
Additional Information
C. Herbert Clemens
Affiliation:
Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210-1174
Email:
clemens@math.ohio-state.edu
Received by editor(s):
October 5, 2010
Received by editor(s) in revised form:
January 15, 2011
Published electronically:
December 19, 2012
