Stability of the parabolic Picard sheaf
Let X be a smooth irreducible complex projective curve of genus g ≥ 2 , and let D = x 1 + ⋯ + x r be a reduced effective divisor on X . Denote by U α ( L ) the moduli space of stable parabolic vector bundles on X of rank n , determinant L of degree d with flag type { { k j i } j = 1 m i } i = 1 r ....
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| Veröffentlicht in: | Proceedings of the Indian Academy of Sciences. Mathematical sciences 2024-11, Vol.134 (2) |
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| creator | Arusha, C Biswas, Indranil |
| description | Let
X
be a smooth irreducible complex projective curve of genus
g
≥
2
, and let
D
=
x
1
+
⋯
+
x
r
be a reduced effective divisor on
X
. Denote by
U
α
(
L
)
the moduli space of stable parabolic vector bundles on
X
of rank
n
, determinant
L
of degree
d
with flag type
{
{
k
j
i
}
j
=
1
m
i
}
i
=
1
r
. Assume that the greatest common divisor of the collection of integers
{
degree
(
L
)
,
{
k
j
i
}
j
=
1
m
i
}
i
=
1
r
}
}
is 1; this condition ensures that there is a Poincaré parabolic vector bundle on
X
×
U
α
(
L
)
. The direct image, to
U
α
(
L
)
, of the vector bundle underlying the Poincaré parabolic vector bundle is called the parabolic Picard sheaf. We prove that the parabolic Picard sheaf is stable. |
| doi_str_mv | 10.1007/s12044-024-00805-2 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_sprin</sourceid><recordid>TN_cdi_proquest_journals_3134326091</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3134326091</sourcerecordid><originalsourceid>FETCH-LOGICAL-p157t-94dbac857a875309f843acc3856cbd5609f76019eca4ef2de74625fc73684f073</originalsourceid><addsrcrecordid>eNpFkE1LxDAQhoMouK7-AU8FD56ik0y-epRFV2FBQT2HNE3cLmVbk-7Bf2-0godhhuHhfeEh5JLBDQPQt5lxEIICLwMGJOVHZAG1RqqVkcfl5hKpYIKfkrOcdwCsFqgW5Pp1ck3Xd9NXNcRq2oZqdMk1Q9_56qXzLrVV3gYXz8lJdH0OF397Sd4f7t9Wj3TzvH5a3W3oyKSeaC3axnkjtTNaItTRCHTeo5HKN61U5aNV6Q7eiRB5G7RQXEavURkRQeOSXM25Yxo-DyFPdjcc0r5UWmQokJcIViicqTymbv8R0j_FwP4YsbMRW4zYXyOW4zeSxFGk</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3134326091</pqid></control><display><type>article</type><title>Stability of the parabolic Picard sheaf</title><source>SpringerLink Journals</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>Indian Academy of Sciences</source><creator>Arusha, C ; Biswas, Indranil</creator><creatorcontrib>Arusha, C ; Biswas, Indranil</creatorcontrib><description>Let
X
be a smooth irreducible complex projective curve of genus
g
≥
2
, and let
D
=
x
1
+
⋯
+
x
r
be a reduced effective divisor on
X
. Denote by
U
α
(
L
)
the moduli space of stable parabolic vector bundles on
X
of rank
n
, determinant
L
of degree
d
with flag type
{
{
k
j
i
}
j
=
1
m
i
}
i
=
1
r
. Assume that the greatest common divisor of the collection of integers
{
degree
(
L
)
,
{
k
j
i
}
j
=
1
m
i
}
i
=
1
r
}
}
is 1; this condition ensures that there is a Poincaré parabolic vector bundle on
X
×
U
α
(
L
)
. The direct image, to
U
α
(
L
)
, of the vector bundle underlying the Poincaré parabolic vector bundle is called the parabolic Picard sheaf. We prove that the parabolic Picard sheaf is stable.</description><identifier>ISSN: 0253-4142</identifier><identifier>EISSN: 0973-7685</identifier><identifier>DOI: 10.1007/s12044-024-00805-2</identifier><language>eng</language><publisher>New Delhi: Springer India</publisher><subject>Mathematics ; Mathematics and Statistics</subject><ispartof>Proceedings of the Indian Academy of Sciences. Mathematical sciences, 2024-11, Vol.134 (2)</ispartof><rights>Indian Academy of Sciences 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000-0002-7594-5477</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/s12044-024-00805-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12044-024-00805-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Arusha, C</creatorcontrib><creatorcontrib>Biswas, Indranil</creatorcontrib><title>Stability of the parabolic Picard sheaf</title><title>Proceedings of the Indian Academy of Sciences. Mathematical sciences</title><addtitle>Proc Math Sci</addtitle><description>Let
X
be a smooth irreducible complex projective curve of genus
g
≥
2
, and let
D
=
x
1
+
⋯
+
x
r
be a reduced effective divisor on
X
. Denote by
U
α
(
L
)
the moduli space of stable parabolic vector bundles on
X
of rank
n
, determinant
L
of degree
d
with flag type
{
{
k
j
i
}
j
=
1
m
i
}
i
=
1
r
. Assume that the greatest common divisor of the collection of integers
{
degree
(
L
)
,
{
k
j
i
}
j
=
1
m
i
}
i
=
1
r
}
}
is 1; this condition ensures that there is a Poincaré parabolic vector bundle on
X
×
U
α
(
L
)
. The direct image, to
U
α
(
L
)
, of the vector bundle underlying the Poincaré parabolic vector bundle is called the parabolic Picard sheaf. We prove that the parabolic Picard sheaf is stable.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0253-4142</issn><issn>0973-7685</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkE1LxDAQhoMouK7-AU8FD56ik0y-epRFV2FBQT2HNE3cLmVbk-7Bf2-0godhhuHhfeEh5JLBDQPQt5lxEIICLwMGJOVHZAG1RqqVkcfl5hKpYIKfkrOcdwCsFqgW5Pp1ck3Xd9NXNcRq2oZqdMk1Q9_56qXzLrVV3gYXz8lJdH0OF397Sd4f7t9Wj3TzvH5a3W3oyKSeaC3axnkjtTNaItTRCHTeo5HKN61U5aNV6Q7eiRB5G7RQXEavURkRQeOSXM25Yxo-DyFPdjcc0r5UWmQokJcIViicqTymbv8R0j_FwP4YsbMRW4zYXyOW4zeSxFGk</recordid><startdate>20241129</startdate><enddate>20241129</enddate><creator>Arusha, C</creator><creator>Biswas, Indranil</creator><general>Springer India</general><general>Springer Nature B.V</general><scope/><orcidid>https://orcid.org/0000-0002-7594-5477</orcidid></search><sort><creationdate>20241129</creationdate><title>Stability of the parabolic Picard sheaf</title><author>Arusha, C ; Biswas, Indranil</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p157t-94dbac857a875309f843acc3856cbd5609f76019eca4ef2de74625fc73684f073</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Arusha, C</creatorcontrib><creatorcontrib>Biswas, Indranil</creatorcontrib><jtitle>Proceedings of the Indian Academy of Sciences. Mathematical sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Arusha, C</au><au>Biswas, Indranil</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability of the parabolic Picard sheaf</atitle><jtitle>Proceedings of the Indian Academy of Sciences. Mathematical sciences</jtitle><stitle>Proc Math Sci</stitle><date>2024-11-29</date><risdate>2024</risdate><volume>134</volume><issue>2</issue><issn>0253-4142</issn><eissn>0973-7685</eissn><abstract>Let
X
be a smooth irreducible complex projective curve of genus
g
≥
2
, and let
D
=
x
1
+
⋯
+
x
r
be a reduced effective divisor on
X
. Denote by
U
α
(
L
)
the moduli space of stable parabolic vector bundles on
X
of rank
n
, determinant
L
of degree
d
with flag type
{
{
k
j
i
}
j
=
1
m
i
}
i
=
1
r
. Assume that the greatest common divisor of the collection of integers
{
degree
(
L
)
,
{
k
j
i
}
j
=
1
m
i
}
i
=
1
r
}
}
is 1; this condition ensures that there is a Poincaré parabolic vector bundle on
X
×
U
α
(
L
)
. The direct image, to
U
α
(
L
)
, of the vector bundle underlying the Poincaré parabolic vector bundle is called the parabolic Picard sheaf. We prove that the parabolic Picard sheaf is stable.</abstract><cop>New Delhi</cop><pub>Springer India</pub><doi>10.1007/s12044-024-00805-2</doi><orcidid>https://orcid.org/0000-0002-7594-5477</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0253-4142 |
| ispartof | Proceedings of the Indian Academy of Sciences. Mathematical sciences, 2024-11, Vol.134 (2) |
| issn | 0253-4142 0973-7685 |
| language | eng |
| recordid | cdi_proquest_journals_3134326091 |
| source | SpringerLink Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Indian Academy of Sciences |
| subjects | Mathematics Mathematics and Statistics |
| title | Stability of the parabolic Picard sheaf |
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