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Complex hyperbolic orbifolds and hybrid lattices
A class of complex hyperbolic lattices in PU (2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see [ 1 , 10 ] and [ 24 ]) in terms of line arrangements. They use branched covers over a suitable blow up of the complete quadrilateral arrangement of lines in P 2 to constru...
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| Published in: | Geometriae dedicata 2023-04, Vol.217 (2), Article 28 |
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| container_title | Geometriae dedicata |
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| creator | Falbel, Elisha Pasquinelli, Irene |
| description | A class of complex hyperbolic lattices in
PU
(2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see [
1
,
10
] and [
24
]) in terms of line arrangements. They use branched covers over a suitable blow up of the complete quadrilateral arrangement of lines in
P
2
to construct the complex hyperbolic surfaces over the orbifolds associated to the lattices. In [
18
] and [
19
], fundamental domains for these lattices have been built by Pasquinelli. Here we show how the fundamental domains can be interpreted in terms of line arrangements as above. This parallel is then applied in the following context. Wells in [
25
] shows that two of the Deligne-Mostow lattices in
PU
(2, 1) can be seen as hybrids of lattices in
PU
(1, 1). Here we show that he implicitly uses the line arrangement and we complete his analysis to all possible pairs of lines. In this way, we show that three more Deligne-Mostow lattices can be given as hybrids. |
| doi_str_mv | 10.1007/s10711-022-00762-y |
| format | article |
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PU
(2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see [
1
,
10
] and [
24
]) in terms of line arrangements. They use branched covers over a suitable blow up of the complete quadrilateral arrangement of lines in
P
2
to construct the complex hyperbolic surfaces over the orbifolds associated to the lattices. In [
18
] and [
19
], fundamental domains for these lattices have been built by Pasquinelli. Here we show how the fundamental domains can be interpreted in terms of line arrangements as above. This parallel is then applied in the following context. Wells in [
25
] shows that two of the Deligne-Mostow lattices in
PU
(2, 1) can be seen as hybrids of lattices in
PU
(1, 1). Here we show that he implicitly uses the line arrangement and we complete his analysis to all possible pairs of lines. In this way, we show that three more Deligne-Mostow lattices can be given as hybrids.</description><identifier>ISSN: 0046-5755</identifier><identifier>EISSN: 1572-9168</identifier><identifier>DOI: 10.1007/s10711-022-00762-y</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Algebraic Geometry ; Convex and Discrete Geometry ; Differential Geometry ; Domains ; Hyperbolic Geometry ; Lattices ; Mathematics ; Mathematics and Statistics ; Original Paper ; Projective Geometry ; Quadrilaterals ; Topology</subject><ispartof>Geometriae dedicata, 2023-04, Vol.217 (2), Article 28</ispartof><rights>The Author(s) 2022</rights><rights>The Author(s) 2022. 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><cites>FETCH-LOGICAL-c244t-5c0c76df457538d751fda4668001976ae0289d4e8fec567a2458c367cee333993</cites><orcidid>0000-0002-4845-4795</orcidid></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>Falbel, Elisha</creatorcontrib><creatorcontrib>Pasquinelli, Irene</creatorcontrib><title>Complex hyperbolic orbifolds and hybrid lattices</title><title>Geometriae dedicata</title><addtitle>Geom Dedicata</addtitle><description>A class of complex hyperbolic lattices in
PU
(2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see [
1
,
10
] and [
24
]) in terms of line arrangements. They use branched covers over a suitable blow up of the complete quadrilateral arrangement of lines in
P
2
to construct the complex hyperbolic surfaces over the orbifolds associated to the lattices. In [
18
] and [
19
], fundamental domains for these lattices have been built by Pasquinelli. Here we show how the fundamental domains can be interpreted in terms of line arrangements as above. This parallel is then applied in the following context. Wells in [
25
] shows that two of the Deligne-Mostow lattices in
PU
(2, 1) can be seen as hybrids of lattices in
PU
(1, 1). Here we show that he implicitly uses the line arrangement and we complete his analysis to all possible pairs of lines. In this way, we show that three more Deligne-Mostow lattices can be given as hybrids.</description><subject>Algebraic Geometry</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Domains</subject><subject>Hyperbolic Geometry</subject><subject>Lattices</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Projective Geometry</subject><subject>Quadrilaterals</subject><subject>Topology</subject><issn>0046-5755</issn><issn>1572-9168</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKxDAUhoMoOI6-gKuC6-jJ9bRLGbzBgBtdh0ySaofOpCYdsG9vtII7V4ef81_gI-SSwTUDwJvMABmjwDktUnM6HZEFU8hpw3R9TBYAUlOFSp2Ss5y3ANAg8gWBVdwNffis3qchpE3sO1fFtOna2Ptc2b0vj03qfNXbcexcyOfkpLV9Dhe_d0le7-9eVo90_fzwtLpdU8elHKly4FD7VpZNUXtUrPVWal0DsAa1DcDrxstQt8EpjZZLVTuh0YUghGgasSRXc--Q4sch5NFs4yHty6ThqDUqLYUsLj67XIo5p9CaIXU7mybDwHyTMTMZU8iYHzJmKiExh3Ix799C-qv-J_UFN4dlbQ</recordid><startdate>20230401</startdate><enddate>20230401</enddate><creator>Falbel, Elisha</creator><creator>Pasquinelli, Irene</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-4845-4795</orcidid></search><sort><creationdate>20230401</creationdate><title>Complex hyperbolic orbifolds and hybrid lattices</title><author>Falbel, Elisha ; Pasquinelli, Irene</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c244t-5c0c76df457538d751fda4668001976ae0289d4e8fec567a2458c367cee333993</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>Domains</topic><topic>Hyperbolic Geometry</topic><topic>Lattices</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Projective Geometry</topic><topic>Quadrilaterals</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Falbel, Elisha</creatorcontrib><creatorcontrib>Pasquinelli, Irene</creatorcontrib><collection>SpringerOpen</collection><collection>CrossRef</collection><jtitle>Geometriae dedicata</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Falbel, Elisha</au><au>Pasquinelli, Irene</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Complex hyperbolic orbifolds and hybrid lattices</atitle><jtitle>Geometriae dedicata</jtitle><stitle>Geom Dedicata</stitle><date>2023-04-01</date><risdate>2023</risdate><volume>217</volume><issue>2</issue><artnum>28</artnum><issn>0046-5755</issn><eissn>1572-9168</eissn><abstract>A class of complex hyperbolic lattices in
PU
(2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see [
1
,
10
] and [
24
]) in terms of line arrangements. They use branched covers over a suitable blow up of the complete quadrilateral arrangement of lines in
P
2
to construct the complex hyperbolic surfaces over the orbifolds associated to the lattices. In [
18
] and [
19
], fundamental domains for these lattices have been built by Pasquinelli. Here we show how the fundamental domains can be interpreted in terms of line arrangements as above. This parallel is then applied in the following context. Wells in [
25
] shows that two of the Deligne-Mostow lattices in
PU
(2, 1) can be seen as hybrids of lattices in
PU
(1, 1). Here we show that he implicitly uses the line arrangement and we complete his analysis to all possible pairs of lines. In this way, we show that three more Deligne-Mostow lattices can be given as hybrids.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10711-022-00762-y</doi><orcidid>https://orcid.org/0000-0002-4845-4795</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Algebraic Geometry Convex and Discrete Geometry Differential Geometry Domains Hyperbolic Geometry Lattices Mathematics Mathematics and Statistics Original Paper Projective Geometry Quadrilaterals Topology |
| title | Complex hyperbolic orbifolds and hybrid lattices |
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