![Für diesen Artikel ist leider kein Bild verfügbar.](/img/platzhalter480px.png)
Flat Rank Two Vector Bundles on Genus Two Curves
Seiten
2019
American Mathematical Society (Verlag)
978-1-4704-3566-0 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-3566-0 (ISBN)
Examines the moduli space of trace-free irreducible rank 2 connections over a curve of genus 2 and the forgetful map towards the moduli space of underlying vector bundles (including unstable bundles), for which they compute a natural Lagrangian rational section.
The authors study the moduli space of trace-free irreducible rank 2 connections over a curve of genus 2 and the forgetful map towards the moduli space of underlying vector bundles (including unstable bundles), for which they compute a natural Lagrangian rational section. As a particularity of the genus $2$ case, connections as above are invariant under the hyperelliptic involution: they descend as rank $2$ logarithmic connections over the Riemann sphere. The authors establish explicit links between the well-known moduli space of the underlying parabolic bundles with the classical approaches by Narasimhan-Ramanan, Tyurin and Bertram. This allows the authors to explain a certain number of geometric phenomena in the considered moduli spaces such as the classical $(16,6)$-configuration of the Kummer surface. The authors also recover a Poincare family due to Bolognesi on a degree 2 cover of the Narasimhan-Ramanan moduli space. They explicitly compute the Hitchin integrable system on the moduli space of Higgs bundles and compare the Hitchin Hamiltonians with those found by van Geemen-Previato. They explicitly describe the isomonodromic foliation in the moduli space of vector bundles with $/mathfrak sl_2$-connection over curves of genus 2 and prove the transversality of the induced flow with the locus of unstable bundles.
The authors study the moduli space of trace-free irreducible rank 2 connections over a curve of genus 2 and the forgetful map towards the moduli space of underlying vector bundles (including unstable bundles), for which they compute a natural Lagrangian rational section. As a particularity of the genus $2$ case, connections as above are invariant under the hyperelliptic involution: they descend as rank $2$ logarithmic connections over the Riemann sphere. The authors establish explicit links between the well-known moduli space of the underlying parabolic bundles with the classical approaches by Narasimhan-Ramanan, Tyurin and Bertram. This allows the authors to explain a certain number of geometric phenomena in the considered moduli spaces such as the classical $(16,6)$-configuration of the Kummer surface. The authors also recover a Poincare family due to Bolognesi on a degree 2 cover of the Narasimhan-Ramanan moduli space. They explicitly compute the Hitchin integrable system on the moduli space of Higgs bundles and compare the Hitchin Hamiltonians with those found by van Geemen-Previato. They explicitly describe the isomonodromic foliation in the moduli space of vector bundles with $/mathfrak sl_2$-connection over curves of genus 2 and prove the transversality of the induced flow with the locus of unstable bundles.
Viktoria Heu, Institut de Recherche Mathematique Avancee (IRMA), Strasbourg, France. Frank Loray, Institut de Recherche Mathematique de Rennes (IRMAR), France.
Introduction
Preliminaries on connections
Hyperelliptic correspondence
Flat vector bundles over $X$
Anticanonical subbundles
Flat parabolic vector bundles over the quotient $X//iota $
The moduli stack $/mathfrak Higgs(X)$ and the Hitchin fibration
The moduli stack $/mathfrak{Con}(X)$
Application to isomonodromic deformations
Bibliography
Erscheinungsdatum | 01.07.2019 |
---|---|
Reihe/Serie | Memoirs of the American Mathematical Society |
Verlagsort | Providence |
Sprache | englisch |
Maße | 178 x 254 mm |
Gewicht | 185 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 1-4704-3566-7 / 1470435667 |
ISBN-13 | 978-1-4704-3566-0 / 9781470435660 |
Zustand | Neuware |
Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Buch | Softcover (2015)
Springer Vieweg (Verlag)
37,99 €