Let $ A=(a_1,\ldots, a_n) $ be a vector of integers which sum to $ k (2g-2+ n) $. The double
ramification cycle $\mathsf {DR} _ {g, A}\in\mathsf {CH}^ g (\mathcal {M} _ {g, n}) $ on the …

For $\theta $ a small generic universal stability condition of degree $0 $ and A a vector of
integers adding up to $-k (2g-2+ n) $, the spaces $\overline {\mathcal {M}} _ {g, A}^\theta …

We introduce the abstract notion of a smoothable fine compactified Jacobian of a nodal
curve, and of a family of nodal curves whose general element is smooth. Then we introduce …

We give an explicit graph formula, in terms of decorated boundary strata classes, for the wall-
crossing of universal Brill-Noether classes. More precisely, fix $ n> 0$ and $ d< g $, and two …

We introduce a general abstract notion of fine compactified Jacobian for nodal curves of
arbitrary genus. We focus on genus and prove combinatorial classification results for fine …

We prove that the pullbacks of the virtual fundamental classes of the Brill-Noether loci under
any Abel-Jacobi section lie in the tautological ring of the moduli space of stable curves. This …

We introduce a new class of fine compactified Jacobians for nodal curves, that we call fine
compactified Jacobians of vine type, or simply fine V-compactified Jacobians. This class is …

The Brill–Noether theory of line bundles on nonsingular algebraic curves is a classical pillar
of XIX century algebraic geometry, which has been rediscovered and reused to prove …

A very interesting story runs in parallel on the moduli space of curves. Fix a vector of integers
A=(a1,···, an) with∑ ai= k (2g− 2):= d. The double ramification cycle DRk g, A is the virtual …