We introduce the notion of an adequate moduli space. The theory of adequate moduli
spaces provides a framework for studying algebraic spaces which geometrically …

For each universal genus‐g polarization μ of degree d, we construct a universal tropical
Jacobian J μ, gtrop as a generalized cone complex over the moduli space of stable pointed …

In this paper we describe compactifications of the universal Jacobian stack of line bundles
over smooth curves obtained by considering open substacks of the moduli stack of torsion …

Using the compactified universal jacobian over the moduli space of stable marked curves,
we give an expression in terms of natural classes of the zero section of in the (rational) …

We study the moduli spaces which classify smooth surfaces along with a complex line
bundle. There are homological stability and Madsen--Weiss type results for these spaces …

We compute the Brauer group of the universal moduli stack of vector bundles on (possibly
marked) smooth curves of genus at least three over the complex numbers. As consequence …

We construct the moduli stack of properly balanced vector bundles on semistable curves
and we determine explicitly its Picard group. As a consequence, we obtain an explicit …

We formulate a tropical analogue of Grothendieck's section conjecture: that for every stable
graph Γ of genus g> 2, and every field k, the generic curve with reduction type Γ over k …

We construct modular compactifications of the universal Jacobian stack over the moduli
stack of reduced curves with marked points depending on stability parameters obtained out …

arXiv:2307.14157v2 [math.AG] 16 Jun 2024 Page 1 Épijournal de Géométrie Algébrique
epiga.episciences.org Special volume in honour of C. Voisin, Article No. 15 (2024) …