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Kirwan surjectivity and Lefschetz–Sommese theorems for a generalized hyperkähler reduction
Let G be a compact Lie group. We study a class of Hamiltonian ( G × S 1 ) -manifolds decorated with a function s with certain equivariance properties, under conditions on the G -action which we call of (semi-)linear type . In this context, a close analogue of hyperkähler reduction is defined, and ou...
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| Published in: | Geometriae dedicata 2023-10, Vol.217 (5), Article 94 |
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| Main Authors: | , , , |
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| container_issue | 5 |
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| container_title | Geometriae dedicata |
| container_volume | 217 |
| creator | Fisher, Jonathan Jeffrey, Lisa Malusà, Alessandro Rayan, Steven |
| description | Let
G
be a compact Lie group. We study a class of Hamiltonian
(
G
×
S
1
)
-manifolds
decorated
with a function
s
with certain equivariance properties, under conditions on the
G
-action which we call of
(semi-)linear type
. In this context, a close analogue of hyperkähler reduction is defined, and our main result establishes surjectivity of an appropriate analogue of Kirwan’s map. As a particular case, our setting includes a class of hyperkähler manifolds with trihamiltonian torus actions, to which our surjectivity result applies. |
| doi_str_mv | 10.1007/s10711-023-00831-w |
| format | article |
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G
be a compact Lie group. We study a class of Hamiltonian
(
G
×
S
1
)
-manifolds
decorated
with a function
s
with certain equivariance properties, under conditions on the
G
-action which we call of
(semi-)linear type
. In this context, a close analogue of hyperkähler reduction is defined, and our main result establishes surjectivity of an appropriate analogue of Kirwan’s map. As a particular case, our setting includes a class of hyperkähler manifolds with trihamiltonian torus actions, to which our surjectivity result applies.</description><identifier>ISSN: 0046-5755</identifier><identifier>EISSN: 1572-9168</identifier><identifier>DOI: 10.1007/s10711-023-00831-w</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Algebraic Geometry ; Convex and Discrete Geometry ; Differential Geometry ; Hamiltonian functions ; Hyperbolic Geometry ; Lie groups ; Manifolds ; Mathematics ; Mathematics and Statistics ; Original Paper ; Projective Geometry ; Reduction ; Topology ; Toruses</subject><ispartof>Geometriae dedicata, 2023-10, Vol.217 (5), Article 94</ispartof><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2023. 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><cites>FETCH-LOGICAL-c270t-18a594fba916ee4448abc21a9e9aace1f90aa6a027e8c30975d415fa30f03a63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Fisher, Jonathan</creatorcontrib><creatorcontrib>Jeffrey, Lisa</creatorcontrib><creatorcontrib>Malusà, Alessandro</creatorcontrib><creatorcontrib>Rayan, Steven</creatorcontrib><title>Kirwan surjectivity and Lefschetz–Sommese theorems for a generalized hyperkähler reduction</title><title>Geometriae dedicata</title><addtitle>Geom Dedicata</addtitle><description>Let
G
be a compact Lie group. We study a class of Hamiltonian
(
G
×
S
1
)
-manifolds
decorated
with a function
s
with certain equivariance properties, under conditions on the
G
-action which we call of
(semi-)linear type
. In this context, a close analogue of hyperkähler reduction is defined, and our main result establishes surjectivity of an appropriate analogue of Kirwan’s map. As a particular case, our setting includes a class of hyperkähler manifolds with trihamiltonian torus actions, to which our surjectivity result applies.</description><subject>Algebraic Geometry</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Hamiltonian functions</subject><subject>Hyperbolic Geometry</subject><subject>Lie groups</subject><subject>Manifolds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Projective Geometry</subject><subject>Reduction</subject><subject>Topology</subject><subject>Toruses</subject><issn>0046-5755</issn><issn>1572-9168</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kE1OwzAQhS0EEqVwAVaWWAfGdhInS1TxJyqxgC2ypsmkSWmSYidU7Yo7cAVuwk04CYYgsWM1m_e-efoYOxZwKgD0mROghQhAqgAgUSJY77CRiLQMUhEnu2wEEMZBpKNonx04twCAVGs5Yo-3lV1jw11vF5R11UvVbTg2OZ9S4bKSuu3n69t9W9fkiHcltZZqx4vWcuRzasjistpSzsvNiuzTx3u5JMst5b1ntc0h2ytw6ejo947Zw-XFw-Q6mN5d3UzOp0EmNXSBSDBKw2KGfixRGIYJzjIpMKUUMSNRpIAYI0hNSab88igPRVSgggIUxmrMTgbsyrbPPbnOLNreNv6jkUkk41TFofApOaQy2zpnqTArW9VoN0aA-bZoBovGWzQ_Fs3al9RQcj7czMn-of9pfQFaRHk4</recordid><startdate>20231001</startdate><enddate>20231001</enddate><creator>Fisher, Jonathan</creator><creator>Jeffrey, Lisa</creator><creator>Malusà, Alessandro</creator><creator>Rayan, Steven</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20231001</creationdate><title>Kirwan surjectivity and Lefschetz–Sommese theorems for a generalized hyperkähler reduction</title><author>Fisher, Jonathan ; Jeffrey, Lisa ; Malusà, Alessandro ; Rayan, Steven</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-18a594fba916ee4448abc21a9e9aace1f90aa6a027e8c30975d415fa30f03a63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebraic Geometry</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Hamiltonian functions</topic><topic>Hyperbolic Geometry</topic><topic>Lie groups</topic><topic>Manifolds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Projective Geometry</topic><topic>Reduction</topic><topic>Topology</topic><topic>Toruses</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fisher, Jonathan</creatorcontrib><creatorcontrib>Jeffrey, Lisa</creatorcontrib><creatorcontrib>Malusà, Alessandro</creatorcontrib><creatorcontrib>Rayan, Steven</creatorcontrib><collection>CrossRef</collection><jtitle>Geometriae dedicata</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fisher, Jonathan</au><au>Jeffrey, Lisa</au><au>Malusà, Alessandro</au><au>Rayan, Steven</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Kirwan surjectivity and Lefschetz–Sommese theorems for a generalized hyperkähler reduction</atitle><jtitle>Geometriae dedicata</jtitle><stitle>Geom Dedicata</stitle><date>2023-10-01</date><risdate>2023</risdate><volume>217</volume><issue>5</issue><artnum>94</artnum><issn>0046-5755</issn><eissn>1572-9168</eissn><abstract>Let
G
be a compact Lie group. We study a class of Hamiltonian
(
G
×
S
1
)
-manifolds
decorated
with a function
s
with certain equivariance properties, under conditions on the
G
-action which we call of
(semi-)linear type
. In this context, a close analogue of hyperkähler reduction is defined, and our main result establishes surjectivity of an appropriate analogue of Kirwan’s map. As a particular case, our setting includes a class of hyperkähler manifolds with trihamiltonian torus actions, to which our surjectivity result applies.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10711-023-00831-w</doi></addata></record> |
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| ispartof | Geometriae dedicata, 2023-10, Vol.217 (5), Article 94 |
| issn | 0046-5755 1572-9168 |
| language | eng |
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| subjects | Algebraic Geometry Convex and Discrete Geometry Differential Geometry Hamiltonian functions Hyperbolic Geometry Lie groups Manifolds Mathematics Mathematics and Statistics Original Paper Projective Geometry Reduction Topology Toruses |
| title | Kirwan surjectivity and Lefschetz–Sommese theorems for a generalized hyperkähler reduction |
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