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Relative Jacobians of elliptic fibrations with reducible fibers

Ana Cristina Lopez
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Abstract

We prove that if $X$ and $S$ are smooth varieties and $f\colon X\to S$ is an elliptic fibration with singular fibers curves of types I$_N$ with $N\geq 1$, II, III and IV, then the relative Jacobian $\hat{f}\colon \bar{M}_{X/S}\to S$ of $f$, defined as the relative moduli space of semistable pure dimension one sheaves of rank 1 and degree 0 on the fibers of $f$, is an elliptic fibration such that all its fibers are irreducible. This extends known results when fibers are integral or of type I$_2$.

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Ana Cristina Lopez. 2004-10-18. Relative Jacobians of elliptic fibrations with reducible fibers. https://arxiv.org/abs/math/0410394

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