dc.contributor.author Dan A. en_US dc.contributor.author Kaur I. en_US dc.date.accessioned 2020-02-07T17:53:31Z dc.date.available 2020-02-07T17:53:31Z dc.date.issued 2019-12-01 dc.identifier.issn 1139-1138 dc.identifier.uri http://hdl.handle.net/20.500.11824/1075 dc.description.abstract Let $\pi_1:\mathcal{X} \to \Delta$ be a flat family of smooth, projective curves of genus $g \ge 2$, degenerating to an irreducible nodal curve $X_0$ with exactly one node. Fix an invertible sheaf $\mathcal{L}$ on $\mathcal{X}$ of relative odd degree. en_US Let $\pi_2:\mathcal{G}(2,\mathcal{L}) \to \Delta$ be the relative Gieseker moduli space of rank $2$ semi-stable vector bundles with determinant $\mathcal{L}$ over $\mathcal{X}$. Since $\pi_2$ is smooth over $\Delta^*$, there exists a canonical family $\widetilde{\rho}_i:\mathbf{J}^i_{\mathcal{G}(2, \mathcal{L})_{\Delta^*}} \to \Delta^{*}$ of $i$-th intermediate Jacobians i.e., for all $t \in \Delta^*$, $(\widetilde{\rho}_i)^{-1}(t)$ is the $i$-th intermediate Jacobian of $\pi_2^{-1}(t)$. There exist different N\'{e}ron models $\overline{\rho}_i:\overline{\mathbf{J}}_{\mathcal{G}(2, \mathcal{L})}^i \to \Delta$ extending $\widetilde{\rho}_i$ to the entire disc $\Delta$, constructed by Clemens, Saito, Schnell, Zucker and Green-Griffiths-Kerr. In this article, we prove that in our setup, the Neron model $\overline{\rho}_i$ is canonical in the sense that the different Neron models coincide and is an analytic fiber space which graphs admissible normal functions. We also show that for $1 \le i \le \max\{2,g-1\}$, the central fiber of $\overline{\rho}_i$ is a fibration over product of copies of $J^k(\mathrm{Jac}(\widetilde{X}_0))$ for certain values of $k$, where $\widetilde{X}_0$ is the normalization of $X_0$. In particular, for $g \ge 5$ and $i=2, 3, 4$, the central fiber of $\overline{\rho}_i$ is a semi-abelian variety. Furthermore, we prove that the $i$-th generalized intermediate Jacobian of the (singular) central fibre of $\pi_2$ is a fibration over the central fibre of the N\'{e}ron model $\overline{\mathbf{J}}^i_{\mathcal{G}(2, \mathcal{L})}$. In fact, for $i=2$ the fibration is an isomorphism. dc.format application/pdf en_US dc.language.iso eng en_US dc.publisher Revista Matemática Complutense en_US dc.relation info:eu-repo/grantAgreement/EC/FP7/615655 en_US dc.relation ES/1PE/SEV-2017-0718 en_US dc.relation EUS/BERC/BERC.2018-2021 en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Torelli theorem en_US dc.subject intermediate Jacobians en_US dc.subject Néron models en_US dc.subject nodal curves en_US dc.subject Gieseker moduli space en_US dc.subject limit mixed Hodge structures. en_US dc.title Neron models of intermediate Jacobians associated to moduli spaces en_US dc.type info:eu-repo/semantics/article en_US dc.type info:eu-repo/semantics/publishedVersion en_US dc.identifier.doi 10.1007/s13163-019-00333-y dc.relation.publisherversion https://link.springer.com/article/10.1007%2Fs13163-019-00333-y en_US
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