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Jacobians and differents of projective varieties

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Abstract

Let X be a reduced and irreducible projective variety of dimension d. Let π:X→Y be a separable noetherian normalization of X and ϕ the canonical morphism Ωd X/k→Ωd L/k. From our main result:

$$J_X \varphi (\pi ^* \Omega ^d _{Y/k} ) = \theta _k (X/Y)\varphi (\Omega ^d _{X/k} )$$

we deduce relations among: complementary module C(X/Y), Kähler different θk(X/Y), Dedekind different θD(X/Y), jacobian ideal JK and ω-jacobian ideal\(\tilde J_X\).

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Authors and Affiliations

  1. Istituto di Matematica, Università di Genova, Via L.B. Alberti 4, 16132, Genova, Italy

    Anna Oneto & Elsa Zatini

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  1. Anna Oneto
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  2. Elsa Zatini
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Oneto, A., Zatini, E. Jacobians and differents of projective varieties. Manuscripta Math 58, 487–495 (1987). https://doi.org/10.1007/BF01277606

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  • DOI: https://doi.org/10.1007/BF01277606

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