Abstract
In this article, we study the irreducible components of the compactified Jacobian of a ribbon X of arithmetic genus g over a smooth curve of genus
. We prove that when
the moduli space of rank 2 semistable vector bundles over
is not an irreducible component and we determine the irreducible components in which it is contained. This answers a question of Chen and Kass in Ref. [Citation2] and completes their results.
Acknowledgments
This article is born as an aside to my doctoral thesis, which is in progress and is about the compactified Jacobian of a primitive multiple curve of multiplicity ≥3. I am grateful to my supervisor, Filippo Viviani, who introduced me to the articles [Citation2] and [Citation4] and more generally to the subject and, moreover, gave me various suggestions about the exposition. I am also grateful to Edoardo Sernesi: my knowledge of one of the key ingredients of the proof, namely Segre-Nagata Theorem (i.e., Fact 2(i)) is due to his unpublished notes about algebraic curves which he distributed confidentially in a preliminary version during a doctoral course about Brill–Noether theory. I would thank also the anonymous referee for his useful comments.
A.m.D.g.
Disclosure statement
No potential conflict of interest was reported by the author.