Infinitesimal Torelli for elliptic surfaces revisited
TL;DR: In this article, a new proof for the infinitesimal Torelli theorem for minimal elliptic surfaces without multiple fibers with Euler number at least 24 for nonconstant j-invariant was given.
About: This article is published in Journal of Pure and Applied Algebra.The article was published on 2022-05-01 and is currently open access. It has received None citations till now. The article focuses on the topics: Mathematics & Infinitesimal.
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01 Jan 2007
TL;DR: The Lefschetz theorem on hyperplane sections and its generalizations have been studied in algebraic cycles and algebraic variabilities as discussed by the authors, and the Leray spectral sequence has been used in the context of hypersurfaces.
Abstract: Introduction. Part I. The Topology of Algebraic Varieties: 1. The Lefschetz theorem on hyperplane sections 2. Lefschetz pencils 3. Monodromy 4. The Leray spectral sequence Part II. Variations of Hodge Structure: 5. Transversality and applications 6. Hodge filtration of hypersurfaces 7. Normal functions and infinitesimal invariants 8. Nori's work Part III. Algebraic Cycles: 9. Chow groups 10. Mumford' theorem and its generalisations 11. The Bloch conjecture and its generalisations References Index.
534 citations
Journal Article•
TL;DR: In this article, the conditions générales d'utilisation (http://www.compositio.nl/) implique l'accord avec les conditions generales de utilisation, i.e., usage commerciale ou impression systématique, constitutive of an infraction pénale.
Abstract: © Foundation Compositio Mathematica, 1988, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
179 citations
TL;DR: In this paper, the Torelli problem for different complex structures on a fixed compact differentiable manifold X is formulated as whether these structures are distinguishable at the cohomology level, for example by the position of the subspace HOOf, f2 k) consisting of classes containing a holomorphic differential k-form.
Abstract: Given different complex structures on a fixed compact differentiable manifold X the Torelli problem for X is whether these structures are distinguishable at the cohomology level, for example by the position of the subspace HOOf, f2 k) ~_ Hk(X, ~) consisting of classes containing a holomorphic differential k-form. Results of this type are classical for Riemann surfaces and complex tori and have been established more recently for various classes of higher dimensional manifolds. An infinitesimal analog of this problem has been systematically formulated by Griffiths in [2]. Namely, given Xs, s~ S a differentiably trivial family of compact K~ihler manifolds parametrized by S, then g = dimH°(X~, f2 k) is independent ofs and one obtains a map P : S~Grass (g, N) assigning s~B°(Xs, f2 k) ~_ Hk(Xs, ¢~). Fixing s e S and letting X =X s, we recall that the differential Os,s ~ Op(s),6r~s~ is computed by composing the Kodaira-Spencer map Q : O~,s--,H~(X, 6)x) with the cup product mapping
23 citations
23 citations