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Flat rank two vector bundles on genus two curves /
"We 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 we compute a natural Lagrangian rational section. As a particularity of the genus 2...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
[2019]
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1247. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 001 | EBOOKCENTRAL_on1104714418 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
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| 020 | |a 1470452499 |q (ebook) | ||
| 020 | |a 9781470452490 |q (electronic bk.) | ||
| 020 | |z 9781470435660 | ||
| 020 | |a 1470435667 | ||
| 020 | |a 9781470435660 | ||
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| 035 | |a (OCoLC)1104714418 |z (OCoLC)1262687338 | ||
| 050 | 4 | |a QA612.6 |b .H48 2019 | |
| 082 | 0 | 4 | |a 514.224 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Heu, Viktoria, |d 1982- | |
| 245 | 1 | 0 | |a Flat rank two vector bundles on genus two curves / |c Viktoria Hue, Frank Loray. |
| 264 | 1 | |a Providence, RI : |b American Mathematical Society, |c [2019] | |
| 264 | 4 | |c ©2019 | |
| 300 | |a 1 online resource (v, 103 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society ; |v number 1247 | |
| 500 | |a Keywords: Vector Bundles, moduli spaces, parabolic connections, Higgs bundles, Kummer surface | ||
| 500 | |a "May 2019 - Volume 259 - Number 1247 (fourth of 8 numbers)." | ||
| 504 | |a Includes bibliographical references. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Chapter 1. Preliminaries on connections; 1.1. Logarithmic connections; 1.2. Twists and trace; 1.3. Projective connections and Riccati foliations; 1.4. Parabolic structures; 1.5. Elementary transformations; 1.6. Stability and moduli spaces; Chapter 2. Hyperelliptic correspondence; 2.1. Topological considerations; 2.2. A direct algebraic approach; Chapter 3. Flat vector bundles over; 3.1. Flatness criterion; 3.2. Semi-stable bundles and the Narasimhan-Ramanan theorem; 3.3. Semi-stable decomposable bundles; 3.4. Semi-stable indecomposable bundles -- 3.5. Unstable and indecomposable: the 6+10 Gunning bundles3.6. Computation of a system of coordinates; Chapter 4. Anticanonical subbundles; 4.1. Tyurin subbundles; 4.2. Extensions of the canonical bundle; 4.3. Tyurin parametrization; Chapter 5. Flat parabolic vector bundles over the quotient /; 5.1. Flatness criterion; 5.2. Dictionary: how special bundles on occur as special bundles on /; 5.3. Semi-stable bundles and projective charts; 5.4. Moving weights and wall-crossing phenomena; 5.5. Galois and Geiser involutions; 5.6. Summary: the moduli stack \BUN( ) -- Chapter 6. The moduli stack ℌ ( ) and the Hitchin fibration6.1. A Poincaré family on the 2-fold cover \HIGGS( / ); 6.2. The Hitchin fibration; 6.3. Explicit Hitchin Hamiltonians on \HIGGS( / ); 6.4. Explicit Hitchin Hamiltonians on \HIGGS( ); 6.5. Comparison to existing formulae; Chapter 7. The moduli stack ℭ ( ); 7.1. An explicit atlas; 7.2. The apparent map on \CON( / ); 7.3. A Lagrangian section of \CON( )→\BUN( ); Chapter 8. Application to isomonodromic deformations; 8.1. Darboux coordinates; 8.2. Hamiltonian system; 8.3. Transversality to the locus of Gunning bundles -- 8.4. Projective structures and Hejhal's theorem | |
| 520 | |a "We 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 we 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. We 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 us to explain a certain number of geometric phenomena in the considered moduli spaces such as the classical (16, 6)-configuration of the Kummer surface. We also recover a Poincarape family due to Bolognesi on a degree 2 cover of the Narasimhan-Ramanan moduli space. We 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. We explicitly describe the isomonodromic foliation in the moduli space of vector bundles with sl2-connection over curves of genus 2 and prove the transversality of the induced flow with the locus of unstable bundles"-- |c Provided by publisher | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Vector bundles. | |
| 650 | 0 | |a Moduli theory. | |
| 650 | 0 | |a Differential equations, Parabolic. | |
| 650 | 0 | |a Arithmetical algebraic geometry. | |
| 650 | 6 | |a Fibrés vectoriels. | |
| 650 | 6 | |a Théorie des modules. | |
| 650 | 6 | |a Équations différentielles paraboliques. | |
| 650 | 6 | |a Géométrie algébrique arithmétique. | |
| 650 | 7 | |a Ecuaciones diferenciales |2 embne | |
| 650 | 0 | 7 | |a Módulos, Teoría de |2 embucm |
| 650 | 0 | 7 | |a Geometría algebraica aritmética |2 embucm |
| 650 | 7 | |a Moduli theory |2 fast | |
| 650 | 7 | |a Differential equations, Parabolic |2 fast | |
| 650 | 7 | |a Arithmetical algebraic geometry |2 fast | |
| 650 | 7 | |a Vector bundles |2 fast | |
| 700 | 1 | |a Loray, Frank, |d 1965- | |
| 758 | |i has work: |a Flat rank two vector bundles on genus two curves (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGff46crrcqFryfTqWX6JC |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Heu, Viktoria. |t Flat Rank Two Vector Bundles on Genus Two Curves. |d Providence : American Mathematical Society, ©2019 |z 9781470435660 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1247. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5788253 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH37445267 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL5788253 | ||
| 938 | |a EBSCOhost |b EBSC |n 2158037 | ||
| 938 | |a YBP Library Services |b YANK |n 300603187 | ||
| 994 | |a 92 |b IZTAP | ||