Abstract
We prove a generalization of the Castelnuovo-de Franchis theorem in the case of p-forms and we apply it to show when, under some natural conditions, a suitable subset of p-forms constructs the Iitaka fibration.
This is a preview of subscription content, log in via an institution to check access.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Campana, F.: Orbifolds, special varieties and classification theory. Ann. Inst. Fourier 54, 499–665 (2004)
Castelnuovo, G.: Sulle superficie aventi il genere aritmetico negativo. Rend. Circ. Mat. Palermo 20, 55–60 (1905)
Catanese, F.: Moduli and classification of irregular Kaehler manifolds (and algebraic varieties) with Albanese general type fibrations. Invent. Math. 104(2), 263–289 (1991)
De Franchis, M.: Sulle superficie algebriche le quali contengono un fascio irrazionale di curve Rend. Circ. Mat. Palermo 20, 49–54 (1905)
Druel, S.: Codimension 1 foliations with numerically trivial canonical class on singular spaces. Duke Math. J. 170(1), 95–203 (2021)
Fujino, O.: Iitaka Conjecture. SpringerBriefs in Mathematics. Springer, Singapore (2020)
González-Alonso, V.: On deformations of curves supported on rigid divisors. Ann. Mat. Pura Appl. 195(1), 111–132 (2016)
Griffiths, P.A.: On the periods of certain rational integrals: I. Ann. Math. 90(3), 460–495 (1969)
Hartshorne, R.: Stable reflexive sheaves. Math. Ann. 254(2), 121–176 (1980)
Kollár, J., Mori, S.: Birational Geometry of Algebraic Varieties Cambridge Tracts in Mathematics, p. 134. Cambridge University Press, Cambridge (1998)
Lazarsfeld, R.: Positivity in algebraic geometry: I-II. Ergebnisse der Mathematik und ihrer Grenzgebiete Folge. Springer-Verlag, Berlin (2004)
Ran, Z.: On subvarieties of abelian varieties. Invent. Math. 62(3), 459–479 (1981)
Rizzi, L., Zucconi, F.: Fujita decomposition and Massey product for fibered varieties. Nagoya Math. J. 247, 624–652 (2022)
Acknowledgements
The authors want to tank Fabrizio Catanese for his encouragement. The first author has been supported by JSPS-Japan Society for the Promotion of Science (Postdoctoral Research Fellowship, The University of Tokyo), by the Institute for Basic Science (IBS-R003-D1) and (IBS-R032-D1), and by European Union funds, NextGenerationEU. The second author has been supported by the grant DIMA Geometry PRIDZUCC and by PRIN 2017 Prot. 2017JTLHJR “Geometric, algebraic and analytic methods in arithmetics”. The authors are members INdAM-GNSAGA.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Rizzi, L., Zucconi, F. A note on a generalization of the Castelnuovo-de Franchis theorem. Rend. Circ. Mat. Palermo, II. Ser (2024). https://doi.org/10.1007/s12215-024-01027-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12215-024-01027-1