Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Variations of the Albanese morphisms

Authors: Gian Pietro Pirola and Francesco Zucconi
Journal: J. Algebraic Geom. 12 (2003), 535-572
Published electronically: January 21, 2003
MathSciNet review: 1966026
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Abstract | References | Additional Information

Abstract: We estimate the number of moduli of an $n$-dimensional variety $X$ through the variation of its Albanese morphism. Refining upon our methods, we work out the classical Castelnuovo bound concerning the number $m$ of moduli of irregular surfaces with birational Albanese map. We interpret our variation by means of higher Abel-Jacobi mappings theory and under the only hypothesis that $X$ has a generically finite morphism to an Abelian variety $A$, we can bound from below the geometrical genus $p_{g}(X)$ in terms of the dimensions of $A$ and $X$. Using the same framework, we characterize the hyperelliptic locus in ${\mathcal{M}}_g$ as the only close subvariety ${\mathcal{H}}$ inside the moduli space of curves with $\dim{\mathcal{H}} \geq 2g-1$ and torsion Abel-Jacobi image of the Ceresa cycle at its generic point.

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Additional Information

Gian Pietro Pirola
Affiliation: Dipartimento di Matematica, Università degli studi di Pavia, Strada Ferrata 1, 27100 Pavia, Italia

Francesco Zucconi
Affiliation: Dipartimento di Matematica e Informatica, Università degli studi di Udine, Via delle Scienze 206, 33100 Udine, Italia

Received by editor(s): December 3, 2000
Published electronically: January 21, 2003
Additional Notes: The first author was partially supported by: (1) Cofin 99: Spazi di moduli e teoria delle rappresentazioni (Murst); (2) GNSAGA; (3) Far 2000 (Pavia): Varietà algebriche, calcolo algebrico, grafi orientati e topologici. The second author was partially supported by: (1) SC.D.I.M.I. cecu 04118 ’99 Ricerca Dipartimentale, Università di Udine; (2) Cofin 99: Spazi di moduli e teoria delle rappresentazioni(Murst); (3) Royal Society-Accademia Nazionale dei Lincei 2000 grant to do research in Great Britain