Higher rank Brill-Noether theory and coherent systems open questions. (English) Zbl 1495.14047
The theory of Brill-Noether deals with the study of the dimension of the space of sections of a vector bundle on an algebraic variety and, among other interesting consequences, it has played a significant role in the study of moduli spaces of curves. In this context, in particular, a coherent system on a smooth irreducible curve \(C\) is a pair \((E,V)\) where \(E\) is a vector bundle on \(C\) of prescribed rank and degree and \(V\) is a vector subspace of the space of sections \(H^0(E)\) of fixed dimension.
The paper presents a wide list of open questions and conjectures on higher rank Brill-Noether theory and on coherent systems. In each section background material is included and an extensive bibliography is provided to the reader interested in deepening the problems discussed.
The paper presents a wide list of open questions and conjectures on higher rank Brill-Noether theory and on coherent systems. In each section background material is included and an extensive bibliography is provided to the reader interested in deepening the problems discussed.
Reviewer: Stefano Pasotti (Brescia)
MSC:
| 14H60 | Vector bundles on curves and their moduli |
| 14H55 | Riemann surfaces; Weierstrass points; gap sequences |
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