Comparison of Poisson structures on moduli spaces
Let X be a complex irreducible smooth projective curve, and let L be an algebraic line bundle on X with a nonzero section σ 0 . Let M denote the moduli space of stable Hitchin pairs ( E , θ ) , where E is an algebraic vector bundle on X of fixed rank r and degree δ , and θ ∈ H 0 ( X , E n d ( E ) ⊗...
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| Veröffentlicht in: | Revista matemática complutense 2023, Vol.36 (1), p.57-72 |
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| creator | Biswas, Indranil Bottacin, Francesco Gómez, Tomás L. |
| description | Let
X
be a complex irreducible smooth projective curve, and let
L
be an algebraic line bundle on
X
with a nonzero section
σ
0
. Let
M
denote the moduli space of stable Hitchin pairs
(
E
,
θ
)
, where
E
is an algebraic vector bundle on
X
of fixed rank
r
and degree
δ
, and
θ
∈
H
0
(
X
,
E
n
d
(
E
)
⊗
K
X
⊗
L
)
. Associating to every stable Hitchin pair its spectral data, an isomorphism of
M
with a moduli space
P
of stable sheaves of pure dimension one on the total space of
K
X
⊗
L
is obtained. Both the moduli spaces
P
and
M
are equipped with algebraic Poisson structures, which are constructed using
σ
0
. Here we prove that the above isomorphism between
P
and
M
preserves the Poisson structures. |
| doi_str_mv | 10.1007/s13163-021-00418-7 |
| format | Article |
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X
be a complex irreducible smooth projective curve, and let
L
be an algebraic line bundle on
X
with a nonzero section
σ
0
. Let
M
denote the moduli space of stable Hitchin pairs
(
E
,
θ
)
, where
E
is an algebraic vector bundle on
X
of fixed rank
r
and degree
δ
, and
θ
∈
H
0
(
X
,
E
n
d
(
E
)
⊗
K
X
⊗
L
)
. Associating to every stable Hitchin pair its spectral data, an isomorphism of
M
with a moduli space
P
of stable sheaves of pure dimension one on the total space of
K
X
⊗
L
is obtained. Both the moduli spaces
P
and
M
are equipped with algebraic Poisson structures, which are constructed using
σ
0
. Here we prove that the above isomorphism between
P
and
M
preserves the Poisson structures.</description><identifier>ISSN: 1139-1138</identifier><identifier>EISSN: 1988-2807</identifier><identifier>DOI: 10.1007/s13163-021-00418-7</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Geometry ; Isomorphism ; Mathematics ; Mathematics and Statistics ; Sheaves ; Topology</subject><ispartof>Revista matemática complutense, 2023, Vol.36 (1), p.57-72</ispartof><rights>The Author(s) 2021</rights><rights>The Author(s) 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-45594220c3faefa1ffd06e364f0db723baf04631506172c414bc00e4f6e72f193</citedby><cites>FETCH-LOGICAL-c363t-45594220c3faefa1ffd06e364f0db723baf04631506172c414bc00e4f6e72f193</cites><orcidid>0000-0002-8497-3760</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s13163-021-00418-7$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13163-021-00418-7$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Biswas, Indranil</creatorcontrib><creatorcontrib>Bottacin, Francesco</creatorcontrib><creatorcontrib>Gómez, Tomás L.</creatorcontrib><title>Comparison of Poisson structures on moduli spaces</title><title>Revista matemática complutense</title><addtitle>Rev Mat Complut</addtitle><description>Let
X
be a complex irreducible smooth projective curve, and let
L
be an algebraic line bundle on
X
with a nonzero section
σ
0
. Let
M
denote the moduli space of stable Hitchin pairs
(
E
,
θ
)
, where
E
is an algebraic vector bundle on
X
of fixed rank
r
and degree
δ
, and
θ
∈
H
0
(
X
,
E
n
d
(
E
)
⊗
K
X
⊗
L
)
. Associating to every stable Hitchin pair its spectral data, an isomorphism of
M
with a moduli space
P
of stable sheaves of pure dimension one on the total space of
K
X
⊗
L
is obtained. Both the moduli spaces
P
and
M
are equipped with algebraic Poisson structures, which are constructed using
σ
0
. Here we prove that the above isomorphism between
P
and
M
preserves the Poisson structures.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Geometry</subject><subject>Isomorphism</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Sheaves</subject><subject>Topology</subject><issn>1139-1138</issn><issn>1988-2807</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kMtKAzEUhoMoWKsv4GrAdfScJE1mllLUCgVd6Dpk0kSmtM2YM7Pw7U0dwZ2bc4H_Ah9j1wi3CGDuCCVqyUEgB1BYc3PCZtjUNRc1mNNyo2x4GfU5uyDaAiwaVasZw2Xa9y53lA5VitVr6uh40pBHP4w5UFW-fdqMu66i3vlAl-wsuh2Fq989Z--PD2_LFV-_PD0v79fcSy0HrhalQQjwMroQHca4AR2kVhE2rRGydRGUlrgAjUZ4har1AEFFHYyI2Mg5u5ly-5w-x0CD3aYxH0qlFUabEt0IXVRiUvmciHKIts_d3uUvi2CPaOyExhY09geNNcUkJxMV8eEj5L_of1zfmeJlYw</recordid><startdate>2023</startdate><enddate>2023</enddate><creator>Biswas, Indranil</creator><creator>Bottacin, Francesco</creator><creator>Gómez, Tomás L.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-8497-3760</orcidid></search><sort><creationdate>2023</creationdate><title>Comparison of Poisson structures on moduli spaces</title><author>Biswas, Indranil ; Bottacin, Francesco ; Gómez, Tomás L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-45594220c3faefa1ffd06e364f0db723baf04631506172c414bc00e4f6e72f193</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Geometry</topic><topic>Isomorphism</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Sheaves</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Biswas, Indranil</creatorcontrib><creatorcontrib>Bottacin, Francesco</creatorcontrib><creatorcontrib>Gómez, Tomás L.</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Revista matemática complutense</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Biswas, Indranil</au><au>Bottacin, Francesco</au><au>Gómez, Tomás L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Comparison of Poisson structures on moduli spaces</atitle><jtitle>Revista matemática complutense</jtitle><stitle>Rev Mat Complut</stitle><date>2023</date><risdate>2023</risdate><volume>36</volume><issue>1</issue><spage>57</spage><epage>72</epage><pages>57-72</pages><issn>1139-1138</issn><eissn>1988-2807</eissn><abstract>Let
X
be a complex irreducible smooth projective curve, and let
L
be an algebraic line bundle on
X
with a nonzero section
σ
0
. Let
M
denote the moduli space of stable Hitchin pairs
(
E
,
θ
)
, where
E
is an algebraic vector bundle on
X
of fixed rank
r
and degree
δ
, and
θ
∈
H
0
(
X
,
E
n
d
(
E
)
⊗
K
X
⊗
L
)
. Associating to every stable Hitchin pair its spectral data, an isomorphism of
M
with a moduli space
P
of stable sheaves of pure dimension one on the total space of
K
X
⊗
L
is obtained. Both the moduli spaces
P
and
M
are equipped with algebraic Poisson structures, which are constructed using
σ
0
. Here we prove that the above isomorphism between
P
and
M
preserves the Poisson structures.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s13163-021-00418-7</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0002-8497-3760</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1139-1138 |
| ispartof | Revista matemática complutense, 2023, Vol.36 (1), p.57-72 |
| issn | 1139-1138 1988-2807 |
| language | eng |
| recordid | cdi_proquest_journals_2767220926 |
| source | Universidad Complutense de Madrid Free Journals; SpringerLink Journals |
| subjects | Algebra Analysis Applications of Mathematics Geometry Isomorphism Mathematics Mathematics and Statistics Sheaves Topology |
| title | Comparison of Poisson structures on moduli spaces |
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