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010 a| 2019023419;

020 a| 9781470435660q| (paperback);

020 z| 9781470452490q| (pdf);

035 a| (WaSeSS)ssj0002189057;

042 a| pcc;

049 a| EREEa| NEHH;

050 00 a| QA612.63b| .H48 2019;

082 00 a| 514/.2242| 23;

100 1 a| Heu, Viktoria,d| 1982-?| UNAUTHORIZED;

245 10 a| Flat rank two vector bundles on genus two curvesh| [electronic resource] /c| Viktoria Heu, Frank Loray.;

260 a| Providence, RI :b| American Mathematical Society,c| [2019];

300 a| v, 103 pages :b| illustrations ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| number 1247;

500 a| "Volume 259, number 1247 (fourth of 8 numbers).";

504 a| Includes bibliographical references.;

505 0 a| Preliminaries on connections -- Hyperelliptic correspondence -- Flat vector bundles over X -- Anticanonical subbundles -- Flat parabolic vector bundles over the quotient X/Î£ -- The moduli stack Higgs(X) and the Hitchin fibration -- The moduli stack Con(X) -- Application to isomonodromic deformations.;

506 a| Available only to authorized users.;

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.;

538 a| Mode of access: World Wide Web;

650 0 a| Vector bundles.=| ^A53897;

650 0 a| Moduli theory.=| ^A121775;

650 0 a| Differential equations, Parabolic.=| ^A58568;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Loray, Frank,d| 1965-?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=5788253;

949 a| CLICK ON WEB ADDRESSw| ASISh| JOYNER188;

949 a| CLICK ON WEB ADDRESSw| ASISh| HSL77;

949 a| CLICK ON WEB ADDRESSw| ASISh| JMUSIC60;

596 a| 1 3 4;

998 a| 5646272;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5646272-1001l| JNETm| JOYNERr| Ys| Yt| JNESSBKu| 7/19/2021x| EBOOKz| JERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5646272-2001l| HSLELECm| HSLr| Ys| Yt| HEBKu| 7/19/2021x| EBOOKz| HERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5646272-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 7/19/2021x| EBOOKz| JERESOURCE;

Flat rank two vector bundles on genus two curves / Viktoria Heu, Frank Loray.

Author/creator	Heu, Viktoria, 1982-
Other author	Loray, Frank, 1965-
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, [2019]
Description	v, 103 pages : illustrations ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Vector bundles. Moduli theory. Differential equations, Parabolic.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; number 1247
Contents	Preliminaries on connections -- Hyperelliptic correspondence -- Flat vector bundles over X -- Anticanonical subbundles -- Flat parabolic vector bundles over the quotient X/Î£ -- The moduli stack Higgs(X) and the Hitchin fibration -- The moduli stack Con(X) -- Application to isomonodromic deformations.
Abstract	"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"-- Provided by publisher.
General note	"Volume 259, number 1247 (fourth of 8 numbers)."
Bibliography note	Includes bibliographical references.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2019023419
ISBN	9781470435660 (paperback)
ISBN	(pdf)

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Flat rank two vector bundles on genus two curves / Viktoria Heu, Frank Loray.

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