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 …

In this paper we describe compactified universal Jacobians, ie, compactifications of the
moduli space of line bundles on smooth curves obtained as moduli spaces of rank $1 …

Let Mg be the moduli space of algebraic curves of genus g. In the early 1980s Harris and
Mumford ([18]) proved that Mg is of general type for g⩾ 24. They used in a crucial way the …

In this article we provide a stack-theoretic framework to study the universal tropical Jacobian
over the moduli space of tropical curves. We develop two approaches to the process of …

EXTREMAL EFFECTIVE DIVISORS ON M Contents 1. Introduction 1 2. Preliminaries on M 3 3.
Geometry of Da 4 4. Extremality of Da 8 5 Page 1 EXTREMAL EFFECTIVE DIVISORS ON M1,n …

The classification of universal Jacobians over the moduli space of curves Page 1 Comment.
Math. Helv. 88 (2013), 587–611 DOI 10.4171/CMH/297 Commentarii Mathematici Helvetici © …

This paper studies the local geometry of compactified Jacobians. The main result is a
presentation of the completed local ring of the compactified Jacobian of a nodal curve as an …

We determine explicitly the Picard groups of the universal Jacobian stack and of its
compactification over the stack of stable curves. Along the way, we prove some results …

Ф и C йжк в P4 в X нд жзйж гви вЙ в иК Я з гл гл и з дгзз а иг гвзижй и б иж м игж о и гв гв
X жгб и д ж (C, X) в И гвк жз анИ гл б иж м игж о и гв гв X а з иг йжк з ан в гв XК Я йз и з …

In this paper, we establish that the singularities of the compactified universal Jacobian are
canonical if the genus is at least four. As a corollary, we determine the Kodaira dimension …