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Campedelli surfaces with fundamental group of order 8
Let S be a Campedelli surface (a minimal surface of general type with p g = 0, K 2 = 2), and an etale cover of degree 8. We prove that the canonical model of Y is a complete intersection of four quadrics . As a consequence, Y is the universal cover of S , the covering group G = Gal( Y / S ) is th...
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| Published in: | Geometriae dedicata 2009-04, Vol.139 (1), p.49-55 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c288t-2234986b96a9e90bd1c45337a516e0cd1637ae099ea44d176981fda0648590153 |
| container_end_page | 55 |
| container_issue | 1 |
| container_start_page | 49 |
| container_title | Geometriae dedicata |
| container_volume | 139 |
| creator | Mendes Lopes, Margarida Pardini, Rita Reid, Miles |
| description | Let
S
be a Campedelli surface (a minimal surface of general type with
p
g
= 0,
K
2
= 2), and
an etale cover of degree 8. We prove that the canonical model
of
Y
is a complete intersection of four quadrics
. As a consequence,
Y
is the universal cover of
S
, the covering group
G
= Gal(
Y
/
S
) is the topological fundamental group
π
1
S
and
G
cannot be the dihedral group
D
4
of order 8. |
| doi_str_mv | 10.1007/s10711-008-9317-2 |
| format | article |
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S
be a Campedelli surface (a minimal surface of general type with
p
g
= 0,
K
2
= 2), and
an etale cover of degree 8. We prove that the canonical model
of
Y
is a complete intersection of four quadrics
. As a consequence,
Y
is the universal cover of
S
, the covering group
G
= Gal(
Y
/
S
) is the topological fundamental group
π
1
S
and
G
cannot be the dihedral group
D
4
of order 8.</description><identifier>ISSN: 0046-5755</identifier><identifier>EISSN: 1572-9168</identifier><identifier>DOI: 10.1007/s10711-008-9317-2</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Algebraic Geometry ; Convex and Discrete Geometry ; Differential Geometry ; Hyperbolic Geometry ; Mathematics ; Mathematics and Statistics ; Original Paper ; Projective Geometry ; Topology</subject><ispartof>Geometriae dedicata, 2009-04, Vol.139 (1), p.49-55</ispartof><rights>Springer Science+Business Media B.V. 2008</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c288t-2234986b96a9e90bd1c45337a516e0cd1637ae099ea44d176981fda0648590153</citedby><cites>FETCH-LOGICAL-c288t-2234986b96a9e90bd1c45337a516e0cd1637ae099ea44d176981fda0648590153</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>Mendes Lopes, Margarida</creatorcontrib><creatorcontrib>Pardini, Rita</creatorcontrib><creatorcontrib>Reid, Miles</creatorcontrib><title>Campedelli surfaces with fundamental group of order 8</title><title>Geometriae dedicata</title><addtitle>Geom Dedicata</addtitle><description>Let
S
be a Campedelli surface (a minimal surface of general type with
p
g
= 0,
K
2
= 2), and
an etale cover of degree 8. We prove that the canonical model
of
Y
is a complete intersection of four quadrics
. As a consequence,
Y
is the universal cover of
S
, the covering group
G
= Gal(
Y
/
S
) is the topological fundamental group
π
1
S
and
G
cannot be the dihedral group
D
4
of order 8.</description><subject>Algebraic Geometry</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Hyperbolic Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Projective Geometry</subject><subject>Topology</subject><issn>0046-5755</issn><issn>1572-9168</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp9j8tOwzAQRS0EEqHwAez8A4YZx88linhJldjA2nJjp6TKS3YixN-Tqqy7mruYc3UPIfcIDwigHzOCRmQAhtkSNeMXpECpObOozCUpAIRiUkt5TW5yPgCA1ZoXRFa-n2KIXdfSvKTG1zHTn3b-ps0yBN_HYfYd3adxmejY0DGFmKi5JVeN73K8-78b8vXy_Fm9se3H63v1tGU1N2ZmnJfCGrWzyttoYRewFrIstZeoItQB1ZojWBu9EAG1sgab4EEJIy2gLDcET711GnNOsXFTanuffh2CO3q7k7dbvd3R2_GV4Scmr7_DPiZ3GJc0rDPPQH8InFlM</recordid><startdate>20090401</startdate><enddate>20090401</enddate><creator>Mendes Lopes, Margarida</creator><creator>Pardini, Rita</creator><creator>Reid, Miles</creator><general>Springer Netherlands</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20090401</creationdate><title>Campedelli surfaces with fundamental group of order 8</title><author>Mendes Lopes, Margarida ; Pardini, Rita ; Reid, Miles</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c288t-2234986b96a9e90bd1c45337a516e0cd1637ae099ea44d176981fda0648590153</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Algebraic Geometry</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Hyperbolic Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Projective Geometry</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mendes Lopes, Margarida</creatorcontrib><creatorcontrib>Pardini, Rita</creatorcontrib><creatorcontrib>Reid, Miles</creatorcontrib><collection>CrossRef</collection><jtitle>Geometriae dedicata</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mendes Lopes, Margarida</au><au>Pardini, Rita</au><au>Reid, Miles</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Campedelli surfaces with fundamental group of order 8</atitle><jtitle>Geometriae dedicata</jtitle><stitle>Geom Dedicata</stitle><date>2009-04-01</date><risdate>2009</risdate><volume>139</volume><issue>1</issue><spage>49</spage><epage>55</epage><pages>49-55</pages><issn>0046-5755</issn><eissn>1572-9168</eissn><abstract>Let
S
be a Campedelli surface (a minimal surface of general type with
p
g
= 0,
K
2
= 2), and
an etale cover of degree 8. We prove that the canonical model
of
Y
is a complete intersection of four quadrics
. As a consequence,
Y
is the universal cover of
S
, the covering group
G
= Gal(
Y
/
S
) is the topological fundamental group
π
1
S
and
G
cannot be the dihedral group
D
4
of order 8.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10711-008-9317-2</doi><tpages>7</tpages></addata></record> |
| fulltext | fulltext |
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| ispartof | Geometriae dedicata, 2009-04, Vol.139 (1), p.49-55 |
| issn | 0046-5755 1572-9168 |
| language | eng |
| recordid | cdi_crossref_primary_10_1007_s10711_008_9317_2 |
| source | Springer Link |
| subjects | Algebraic Geometry Convex and Discrete Geometry Differential Geometry Hyperbolic Geometry Mathematics Mathematics and Statistics Original Paper Projective Geometry Topology |
| title | Campedelli surfaces with fundamental group of order 8 |
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