Bounds on the Picard rank of toric Fano varieties with minimal curve constraints
We study the Picard rank of smooth toric Fano varieties possessing families of minimal rational curves of given degree. We discuss variants of a conjecture of Chen-Fu-Hwang and prove a version of their statement that recovers the original conjecture in sufficiently high dimension. We also prove new...
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| creator | Beheshti, Roya Wormleighton, Ben |
| description | We study the Picard rank of smooth toric Fano varieties possessing families
of minimal rational curves of given degree. We discuss variants of a conjecture
of Chen-Fu-Hwang and prove a version of their statement that recovers the
original conjecture in sufficiently high dimension. We also prove new cases of
the original conjecture for high degrees in all dimensions. Our main tools come
from toric Mori theory and the combinatorics of Fano polytopes. |
| doi_str_mv | 10.48550/arxiv.2202.01852 |
| format | Article |
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of minimal rational curves of given degree. We discuss variants of a conjecture
of Chen-Fu-Hwang and prove a version of their statement that recovers the
original conjecture in sufficiently high dimension. We also prove new cases of
the original conjecture for high degrees in all dimensions. Our main tools come
from toric Mori theory and the combinatorics of Fano polytopes.</description><identifier>DOI: 10.48550/arxiv.2202.01852</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry</subject><creationdate>2022-02</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2202.01852$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2202.01852$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Beheshti, Roya</creatorcontrib><creatorcontrib>Wormleighton, Ben</creatorcontrib><title>Bounds on the Picard rank of toric Fano varieties with minimal curve constraints</title><description>We study the Picard rank of smooth toric Fano varieties possessing families
of minimal rational curves of given degree. We discuss variants of a conjecture
of Chen-Fu-Hwang and prove a version of their statement that recovers the
original conjecture in sufficiently high dimension. We also prove new cases of
the original conjecture for high degrees in all dimensions. Our main tools come
from toric Mori theory and the combinatorics of Fano polytopes.</description><subject>Mathematics - Algebraic Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz71OwzAUhmEvDKhwAUycG0iI_2JnLBUFpEp06B6d2Ceq1dZGjhvg7oHC9G2vvoexO97UymrdPGD-DHMtRCPqhlstrtn2MZ2jnyBFKHuCbXCYPWSMB0gjlJSDgzXGBDPmQCXQBB-h7OEUYjjhEdw5zwQuxalkDLFMN-xqxONEt_-7YLv10271Um3enl9Xy02FrREVGjdo3nri2HGykkZpWmXQOlLWWO1HS6Klzg9e2sF2ysnOauWHVknpZScX7P4veyH17_nnTf7qf2n9hSa_AUeLScE</recordid><startdate>20220203</startdate><enddate>20220203</enddate><creator>Beheshti, Roya</creator><creator>Wormleighton, Ben</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220203</creationdate><title>Bounds on the Picard rank of toric Fano varieties with minimal curve constraints</title><author>Beheshti, Roya ; Wormleighton, Ben</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a672-a7cb516de1a91e83ef37647a8ce48785df8e26e9dbd38b894c39854db6433d393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Algebraic Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Beheshti, Roya</creatorcontrib><creatorcontrib>Wormleighton, Ben</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Beheshti, Roya</au><au>Wormleighton, Ben</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bounds on the Picard rank of toric Fano varieties with minimal curve constraints</atitle><date>2022-02-03</date><risdate>2022</risdate><abstract>We study the Picard rank of smooth toric Fano varieties possessing families
of minimal rational curves of given degree. We discuss variants of a conjecture
of Chen-Fu-Hwang and prove a version of their statement that recovers the
original conjecture in sufficiently high dimension. We also prove new cases of
the original conjecture for high degrees in all dimensions. Our main tools come
from toric Mori theory and the combinatorics of Fano polytopes.</abstract><doi>10.48550/arxiv.2202.01852</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Algebraic Geometry |
| title | Bounds on the Picard rank of toric Fano varieties with minimal curve constraints |
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