Loading…

On the geometry of a smooth model of a fibre product of families of K3 surfaces

The Hodge conjecture on algebraic cycles is proved for a smooth projective model of a fibre product of nonisotrivial 1-parameter families of K3 surfaces (possibly with degeneracies) over a smooth projective curve under the assumption that, for generic geometric fibres and , the ring is an imaginary...

Full description

Saved in:

Bibliographic Details
Published in:	Sbornik. Mathematics 2014-01, Vol.205 (2), p.269-276
Main Author:	Nikol'skaya, O. V.
Format:	Article
Language:	English
Subjects:	Algebra Curves (geometry) DIAGRAMS FIBERS Fibre Fibres Fields (mathematics) GEOMETRY Hodge conjecture K3 surface MATHEMATICAL METHODS AND COMPUTING MATHEMATICAL MODELS MATHEMATICAL OPERATORS MATHEMATICAL SOLUTIONS MATHEMATICAL SPACE Number theory SURFACES
Citations:	Items that this one cites Items that cite this one
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

cited_by	cdi_FETCH-LOGICAL-c362t-4b3aca64cf63ac6bdc5559816ea47f1bd8d571cbec27896f799fb81fc7e0cc6e3
cites	cdi_FETCH-LOGICAL-c362t-4b3aca64cf63ac6bdc5559816ea47f1bd8d571cbec27896f799fb81fc7e0cc6e3
container_end_page	276
container_issue	2
container_start_page	269
container_title	Sbornik. Mathematics
container_volume	205
creator	Nikol'skaya, O. V.
description	The Hodge conjecture on algebraic cycles is proved for a smooth projective model of a fibre product of nonisotrivial 1-parameter families of K3 surfaces (possibly with degeneracies) over a smooth projective curve under the assumption that, for generic geometric fibres and , the ring is an imaginary quadratic field, , and is a totally real field or else . Bibliography: 10 titles.
doi_str_mv	10.1070/SM2014v205n02ABEH004374
format	article
fullrecord	<record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1744719939</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1744719939</sourcerecordid><originalsourceid>FETCH-LOGICAL-c362t-4b3aca64cf63ac6bdc5559816ea47f1bd8d571cbec27896f799fb81fc7e0cc6e3</originalsourceid><addsrcrecordid>eNqFkEtPwzAQhCMEEuXxG4jEhUvAr9jJsVRAEUU9AGfL2axpqiQutoPUf0-qcEWcdjT6ZrU7SXJFyS0lity9vTJCxTcjeU_Y_P5hSYjgShwlMypkkYmCsONREymyXFJ5mpyFsCWE5IwWs2S97tO4wfQTXYfR71NnU5OGzrm4STtXYzs5tqk8pjvv6gHiwbKma9oGw0G_8DQM3hrAcJGcWNMGvPyd58nH48P7Ypmt1k_Pi_kqAy5ZzETFDRgpwMpRyKqGPM_Lgko0Qlla1UWdKwoVAlNFKa0qS1sV1IJCAiCRnyfX014XYqMDNBFhA67vEaJmjMtc8WKkbiZqPPxrwBB11wTAtjU9uiFoqoRQtCx5OaJqQsG7EDxavfNNZ_xeU6IPRes_ih6TfEo2bqe3bvD9-Pi_qR_PHYBP</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1744719939</pqid></control><display><type>article</type><title>On the geometry of a smooth model of a fibre product of families of K3 surfaces</title><source>Institute of Physics:Jisc Collections:IOP Publishing Read and Publish 2024-2025 (Reading List)</source><creator>Nikol'skaya, O. V.</creator><creatorcontrib>Nikol'skaya, O. V.</creatorcontrib><description>The Hodge conjecture on algebraic cycles is proved for a smooth projective model of a fibre product of nonisotrivial 1-parameter families of K3 surfaces (possibly with degeneracies) over a smooth projective curve under the assumption that, for generic geometric fibres and , the ring is an imaginary quadratic field, , and is a totally real field or else . Bibliography: 10 titles.</description><identifier>ISSN: 1064-5616</identifier><identifier>EISSN: 1468-4802</identifier><identifier>DOI: 10.1070/SM2014v205n02ABEH004374</identifier><language>eng</language><publisher>United States: London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences</publisher><subject>Algebra ; Curves (geometry) ; DIAGRAMS ; FIBERS ; Fibre ; Fibres ; Fields (mathematics) ; GEOMETRY ; Hodge conjecture ; K3 surface ; MATHEMATICAL METHODS AND COMPUTING ; MATHEMATICAL MODELS ; MATHEMATICAL OPERATORS ; MATHEMATICAL SOLUTIONS ; MATHEMATICAL SPACE ; Number theory ; SURFACES</subject><ispartof>Sbornik. Mathematics, 2014-01, Vol.205 (2), p.269-276</ispartof><rights>2014 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c362t-4b3aca64cf63ac6bdc5559816ea47f1bd8d571cbec27896f799fb81fc7e0cc6e3</citedby><cites>FETCH-LOGICAL-c362t-4b3aca64cf63ac6bdc5559816ea47f1bd8d571cbec27896f799fb81fc7e0cc6e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27923,27924</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/22365738$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Nikol'skaya, O. V.</creatorcontrib><title>On the geometry of a smooth model of a fibre product of families of K3 surfaces</title><title>Sbornik. Mathematics</title><addtitle>MSB</addtitle><addtitle>Sb. Math</addtitle><description>The Hodge conjecture on algebraic cycles is proved for a smooth projective model of a fibre product of nonisotrivial 1-parameter families of K3 surfaces (possibly with degeneracies) over a smooth projective curve under the assumption that, for generic geometric fibres and , the ring is an imaginary quadratic field, , and is a totally real field or else . Bibliography: 10 titles.</description><subject>Algebra</subject><subject>Curves (geometry)</subject><subject>DIAGRAMS</subject><subject>FIBERS</subject><subject>Fibre</subject><subject>Fibres</subject><subject>Fields (mathematics)</subject><subject>GEOMETRY</subject><subject>Hodge conjecture</subject><subject>K3 surface</subject><subject>MATHEMATICAL METHODS AND COMPUTING</subject><subject>MATHEMATICAL MODELS</subject><subject>MATHEMATICAL OPERATORS</subject><subject>MATHEMATICAL SOLUTIONS</subject><subject>MATHEMATICAL SPACE</subject><subject>Number theory</subject><subject>SURFACES</subject><issn>1064-5616</issn><issn>1468-4802</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNqFkEtPwzAQhCMEEuXxG4jEhUvAr9jJsVRAEUU9AGfL2axpqiQutoPUf0-qcEWcdjT6ZrU7SXJFyS0lity9vTJCxTcjeU_Y_P5hSYjgShwlMypkkYmCsONREymyXFJ5mpyFsCWE5IwWs2S97tO4wfQTXYfR71NnU5OGzrm4STtXYzs5tqk8pjvv6gHiwbKma9oGw0G_8DQM3hrAcJGcWNMGvPyd58nH48P7Ypmt1k_Pi_kqAy5ZzETFDRgpwMpRyKqGPM_Lgko0Qlla1UWdKwoVAlNFKa0qS1sV1IJCAiCRnyfX014XYqMDNBFhA67vEaJmjMtc8WKkbiZqPPxrwBB11wTAtjU9uiFoqoRQtCx5OaJqQsG7EDxavfNNZ_xeU6IPRes_ih6TfEo2bqe3bvD9-Pi_qR_PHYBP</recordid><startdate>20140101</startdate><enddate>20140101</enddate><creator>Nikol'skaya, O. V.</creator><general>London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope><scope>OTOTI</scope></search><sort><creationdate>20140101</creationdate><title>On the geometry of a smooth model of a fibre product of families of K3 surfaces</title><author>Nikol'skaya, O. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c362t-4b3aca64cf63ac6bdc5559816ea47f1bd8d571cbec27896f799fb81fc7e0cc6e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Algebra</topic><topic>Curves (geometry)</topic><topic>DIAGRAMS</topic><topic>FIBERS</topic><topic>Fibre</topic><topic>Fibres</topic><topic>Fields (mathematics)</topic><topic>GEOMETRY</topic><topic>Hodge conjecture</topic><topic>K3 surface</topic><topic>MATHEMATICAL METHODS AND COMPUTING</topic><topic>MATHEMATICAL MODELS</topic><topic>MATHEMATICAL OPERATORS</topic><topic>MATHEMATICAL SOLUTIONS</topic><topic>MATHEMATICAL SPACE</topic><topic>Number theory</topic><topic>SURFACES</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nikol'skaya, O. V.</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>OSTI.GOV</collection><jtitle>Sbornik. Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nikol'skaya, O. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the geometry of a smooth model of a fibre product of families of K3 surfaces</atitle><jtitle>Sbornik. Mathematics</jtitle><stitle>MSB</stitle><addtitle>Sb. Math</addtitle><date>2014-01-01</date><risdate>2014</risdate><volume>205</volume><issue>2</issue><spage>269</spage><epage>276</epage><pages>269-276</pages><issn>1064-5616</issn><eissn>1468-4802</eissn><abstract>The Hodge conjecture on algebraic cycles is proved for a smooth projective model of a fibre product of nonisotrivial 1-parameter families of K3 surfaces (possibly with degeneracies) over a smooth projective curve under the assumption that, for generic geometric fibres and , the ring is an imaginary quadratic field, , and is a totally real field or else . Bibliography: 10 titles.</abstract><cop>United States</cop><pub>London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences</pub><doi>10.1070/SM2014v205n02ABEH004374</doi><tpages>8</tpages></addata></record>
fulltext	fulltext
identifier	ISSN: 1064-5616
ispartof	Sbornik. Mathematics, 2014-01, Vol.205 (2), p.269-276
issn	1064-5616 1468-4802
language	eng
recordid	cdi_proquest_miscellaneous_1744719939
source	Institute of Physics:Jisc Collections:IOP Publishing Read and Publish 2024-2025 (Reading List)
subjects	Algebra Curves (geometry) DIAGRAMS FIBERS Fibre Fibres Fields (mathematics) GEOMETRY Hodge conjecture K3 surface MATHEMATICAL METHODS AND COMPUTING MATHEMATICAL MODELS MATHEMATICAL OPERATORS MATHEMATICAL SOLUTIONS MATHEMATICAL SPACE Number theory SURFACES
title	On the geometry of a smooth model of a fibre product of families of K3 surfaces
url	http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-11T13%3A11%3A07IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20geometry%20of%20a%20smooth%20model%20of%20a%20fibre%20product%20of%20families%20of%20K3%20surfaces&rft.jtitle=Sbornik.%20Mathematics&rft.au=Nikol'skaya,%20O.%20V.&rft.date=2014-01-01&rft.volume=205&rft.issue=2&rft.spage=269&rft.epage=276&rft.pages=269-276&rft.issn=1064-5616&rft.eissn=1468-4802&rft_id=info:doi/10.1070/SM2014v205n02ABEH004374&rft_dat=%3Cproquest_cross%3E1744719939%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c362t-4b3aca64cf63ac6bdc5559816ea47f1bd8d571cbec27896f799fb81fc7e0cc6e3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1744719939&rft_id=info:pmid/&rfr_iscdi=true