On the Tropicalization of the Hilbert Scheme

On the Tropicalization of the Hilbert Scheme

In this article we study the tropicalization of the Hilbert scheme and its suitability as a parameter space for tropical varieties. We prove that the points of the tropicalization of the Hilbert scheme have a tropical variety naturally associated to them. To prove this, we find a bound on the degree...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2009-12
Hauptverfasser: Alessandrini, Daniele, Nesci, Michele
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical analysis
Polynomials
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Alessandrini, Daniele
Nesci, Michele
description In this article we study the tropicalization of the Hilbert scheme and its suitability as a parameter space for tropical varieties. We prove that the points of the tropicalization of the Hilbert scheme have a tropical variety naturally associated to them. To prove this, we find a bound on the degree of the elements of a tropical basis of an ideal in terms of its Hilbert polynomial. As corollary, we prove that the set of tropical varieties defined over an algebraically closed valued field only depends on the characteristic pair of the field and the image group of the valuation. In conclusion, we examine some simple examples that suggest that the definition of tropical variety should include more structure than what is currently considered.
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2090520500</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2090520500</sourcerecordid><originalsourceid>FETCH-proquest_journals_20905205003</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mTQ8c9TKMlIVQgpyi_ITE7MyaxKLMnMz1PITwMLe2TmJKUWlSgEJ2ek5qbyMLCmJeYUp_JCaW4GZTfXEGcP3YKi_MLS1OKS-Kz80qI8oFS8kYGlgamRgamBgTFxqgBTeTEO</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2090520500</pqid></control><display><type>article</type><title>On the Tropicalization of the Hilbert Scheme</title><source>Free E- Journals</source><creator>Alessandrini, Daniele ; Nesci, Michele</creator><creatorcontrib>Alessandrini, Daniele ; Nesci, Michele</creatorcontrib><description>In this article we study the tropicalization of the Hilbert scheme and its suitability as a parameter space for tropical varieties. We prove that the points of the tropicalization of the Hilbert scheme have a tropical variety naturally associated to them. To prove this, we find a bound on the degree of the elements of a tropical basis of an ideal in terms of its Hilbert polynomial. As corollary, we prove that the set of tropical varieties defined over an algebraically closed valued field only depends on the characteristic pair of the field and the image group of the valuation. In conclusion, we examine some simple examples that suggest that the definition of tropical variety should include more structure than what is currently considered.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Mathematical analysis ; Polynomials</subject><ispartof>arXiv.org, 2009-12</ispartof><rights>2009. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>776,780</link.rule.ids></links><search><creatorcontrib>Alessandrini, Daniele</creatorcontrib><creatorcontrib>Nesci, Michele</creatorcontrib><title>On the Tropicalization of the Hilbert Scheme</title><title>arXiv.org</title><description>In this article we study the tropicalization of the Hilbert scheme and its suitability as a parameter space for tropical varieties. We prove that the points of the tropicalization of the Hilbert scheme have a tropical variety naturally associated to them. To prove this, we find a bound on the degree of the elements of a tropical basis of an ideal in terms of its Hilbert polynomial. As corollary, we prove that the set of tropical varieties defined over an algebraically closed valued field only depends on the characteristic pair of the field and the image group of the valuation. In conclusion, we examine some simple examples that suggest that the definition of tropical variety should include more structure than what is currently considered.</description><subject>Mathematical analysis</subject><subject>Polynomials</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mTQ8c9TKMlIVQgpyi_ITE7MyaxKLMnMz1PITwMLe2TmJKUWlSgEJ2ek5qbyMLCmJeYUp_JCaW4GZTfXEGcP3YKi_MLS1OKS-Kz80qI8oFS8kYGlgamRgamBgTFxqgBTeTEO</recordid><startdate>20091201</startdate><enddate>20091201</enddate><creator>Alessandrini, Daniele</creator><creator>Nesci, Michele</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20091201</creationdate><title>On the Tropicalization of the Hilbert Scheme</title><author>Alessandrini, Daniele ; Nesci, Michele</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20905205003</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Mathematical analysis</topic><topic>Polynomials</topic><toplevel>online_resources</toplevel><creatorcontrib>Alessandrini, Daniele</creatorcontrib><creatorcontrib>Nesci, Michele</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Alessandrini, Daniele</au><au>Nesci, Michele</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>On the Tropicalization of the Hilbert Scheme</atitle><jtitle>arXiv.org</jtitle><date>2009-12-01</date><risdate>2009</risdate><eissn>2331-8422</eissn><abstract>In this article we study the tropicalization of the Hilbert scheme and its suitability as a parameter space for tropical varieties. We prove that the points of the tropicalization of the Hilbert scheme have a tropical variety naturally associated to them. To prove this, we find a bound on the degree of the elements of a tropical basis of an ideal in terms of its Hilbert polynomial. As corollary, we prove that the set of tropical varieties defined over an algebraically closed valued field only depends on the characteristic pair of the field and the image group of the valuation. In conclusion, we examine some simple examples that suggest that the definition of tropical variety should include more structure than what is currently considered.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2009-12
issn 2331-8422
language eng
recordid cdi_proquest_journals_2090520500
source Free E- Journals
subjects Mathematical analysis
Polynomials
title On the Tropicalization of the Hilbert Scheme
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-28T07%3A34%3A59IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=On%20the%20Tropicalization%20of%20the%20Hilbert%20Scheme&rft.jtitle=arXiv.org&rft.au=Alessandrini,%20Daniele&rft.date=2009-12-01&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2090520500%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2090520500&rft_id=info:pmid/&rfr_iscdi=true