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The resolution of the degree‐2 Abel‐Jacobi map for nodal curves‐I
Author(s) -
Pacini Marco
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200339
Subject(s) - mathematics , jacobian matrix and determinant , degree (music) , smoothing , nodal , mathematical analysis , pure mathematics , statistics , medicine , physics , acoustics , anatomy
Let f : C → B be a regular local smoothing of a nodal curve. In this paper, we find a modular description of the Néron maps associated to Abel‐Jacobi maps with values in Esteves's fine compactified Jacobian and with source the B ‐smooth locus of either the double product of C over B or the degree‐2 Hilbert scheme of the family f . This is the first of a series of two papers dedicated to the construction of a resolution of the degree‐2 Abel‐Jacobi map for a regular smoothing of a nodal curve.