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dc.contributor.authorDan A.en_US
dc.contributor.authorKaur I.en_US
dc.date.accessioned2020-02-07T17:53:31Z
dc.date.available2020-02-07T17:53:31Z
dc.date.issued2019-12-01
dc.identifier.issn1139-1138
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1075
dc.description.abstractLet $\pi_1:\mathcal{X} \to \Delta$ 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. 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.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.publisherRevista Matemática Complutenseen_US
dc.relationinfo:eu-repo/grantAgreement/EC/FP7/615655en_US
dc.relationES/1PE/SEV-2017-0718en_US
dc.relationEUS/BERC/BERC.2018-2021en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectTorelli theoremen_US
dc.subjectintermediate Jacobiansen_US
dc.subjectNéron modelsen_US
dc.subjectnodal curvesen_US
dc.subjectGieseker moduli spaceen_US
dc.subjectlimit mixed Hodge structures.en_US
dc.titleNeron models of intermediate Jacobians associated to moduli spacesen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.typeinfo:eu-repo/semantics/publishedVersionen_US
dc.identifier.doi10.1007/s13163-019-00333-y
dc.relation.publisherversionhttps://link.springer.com/article/10.1007%2Fs13163-019-00333-yen_US


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