Fine compactified Jacobians

Abstract

We study Esteves's fine compactified Jacobians for nodal curves. We give a proof of the fact that, for a one-parameter regular local smoothing of a nodal curve $X$, the relative smooth locus of a relative fine compactified Jacobian is isomorphic to the Néron model of the Jacobian of the general fiber, and thus it provides a modular compactification of it. We show that each fine compactified Jacobian of $X$ admits a stratification in terms of certain fine compactified Jacobians of partial normalizations of $X$ and, moreover, that it can be realized as a quotient of the smooth locus of a suitable fine compactified Jacobian of the total blowup of $X$. Finally, we determine when a fine compactified Jacobian is isomorphic to the corresponding Oda-Seshadri's coarse compactified Jacobian.

35 pages; final version, to appear in Math. Nach

References in corpus (3)

• Compactified Jacobians of Néron type
• Le lemme fondamental pour les groupes unitaires
• Combinatorial aspects of nodal curves

Cited by in corpus (15)

• Compactified Jacobians of Néron type
• The universal tropical Jacobian and the skeleton of the Esteves' universal Jacobian
• Fourier-Mukai and autoduality for compactified Jacobians II
• GIT for polarized curves
• Two ways to degenerate the Jacobian are the same
• Extensions of the universal theta divisor
• The Local Structure of Compactified Jacobians
• A support theorem for Hilbert schemes of planar curves, II
• Compactified Jacobians as Mumford models
• Tropicalization of the universal Jacobian
• A support theorem for the Hitchin fibration: the case of $G{L}_n$ and $K_C$
• Clifford representatives via the uniform algebraic rank
• Stability conditions for line bundles on nodal curves
• Orbifold Euler Characteristics of Compactified Jacobians
• An explicit semi-factorial compactification of the Néron model