Geometry of Genus One Fine Compactified Universal Jacobians

• DOI: 10.1093/imrn/rnac094
• Publication Date: 2022-04-14T11:11:35Z
• Authors: Nicola Pagani; Orsola Tommasi
• Keywords: Mathematics - Algebraic Geometry; FOS: Mathematics; Algebraic Topology (math.AT); compactified jacobians, moduli, curves, cohomology; Mathematics - Algebraic Topology; Algebraic Geometry (math.AG); 14H10, 14H40, 14K10, 14F25

Abstract We introduce a general abstract notion of fine compactified Jacobian for nodal curves arbitrary genus. focus on genus $1$ and prove combinatorial classification results Jacobians in the case single curve universal family $\overline {{\mathcal {C}}}_{1,n} / \overline {M}}}_{1,n}$ over moduli space stable pointed curves. show that if can be extended to smoothing curve, then it described as sheaves with respect some polarisation. In we construct new examples Jacobians. Then give formula Hodge Betti numbers each {J}}}^{d}_{1,n}$ their even cohomology is algebraic.