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A bound on certain local cohomology modules and application to ample divisors
We consider a positively graded noetherian domain R = ⊕n∈No Rn for which R0 is essentially of finite type over a perfect field K of positive characteristic and we assume that the generic fibre of the natural morphism π: Y = Proj(R) → Y 0 = Spec(R 0) is geometrically connected, geometrically normal a...
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| Published in: | Nagoya mathematical journal 2001-09, Vol.163, p.87-106 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c416t-bd58405d554e0d26adfce9e6b081a9b719481e6f149fe06d5ce00f6d10aaaabd3 |
| container_end_page | 106 |
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| container_start_page | 87 |
| container_title | Nagoya mathematical journal |
| container_volume | 163 |
| creator | Albertini, Claudia Brodmann, Markus |
| description | We consider a positively graded noetherian domain R = ⊕n∈No
Rn
for which R0
is essentially of finite type over a perfect field K of positive characteristic and we assume that the generic fibre of the natural morphism π: Y = Proj(R) → Y
0 = Spec(R
0) is geometrically connected, geometrically normal and of dimension > 1. Then we give bounds on the “ranks” of the n-th homogeneous part H
2(R)n of the second local cohomology module of R with respect to R
+:= ⊕m>0
Rm
for n < 0. If Y is in addition normal, we shall see that the R
0-modules H
2
R
+ (R)n
are torsion-free for all n < 0 and in this case our bounds on the ranks furnish a vanishing result. From these results we get bounds on the first cohomology of ample invertible sheaves in positive characteristic. |
| doi_str_mv | 10.1017/S0027763000007923 |
| format | article |
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Rn
for which R0
is essentially of finite type over a perfect field K of positive characteristic and we assume that the generic fibre of the natural morphism π: Y = Proj(R) → Y
0 = Spec(R
0) is geometrically connected, geometrically normal and of dimension > 1. Then we give bounds on the “ranks” of the n-th homogeneous part H
2(R)n of the second local cohomology module of R with respect to R
+:= ⊕m>0
Rm
for n < 0. If Y is in addition normal, we shall see that the R
0-modules H
2
R
+ (R)n
are torsion-free for all n < 0 and in this case our bounds on the ranks furnish a vanishing result. From these results we get bounds on the first cohomology of ample invertible sheaves in positive characteristic.</description><identifier>ISSN: 0027-7630</identifier><identifier>EISSN: 2152-6842</identifier><identifier>DOI: 10.1017/S0027763000007923</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>13D45 ; 14B15</subject><ispartof>Nagoya mathematical journal, 2001-09, Vol.163, p.87-106</ispartof><rights>Copyright © Editorial Board of Nagoya Mathematical Journal 2000</rights><rights>Copyright 2001 Editorial Board, Nagoya Mathematical Journal</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c416t-bd58405d554e0d26adfce9e6b081a9b719481e6f149fe06d5ce00f6d10aaaabd3</citedby><cites>FETCH-LOGICAL-c416t-bd58405d554e0d26adfce9e6b081a9b719481e6f149fe06d5ce00f6d10aaaabd3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,926,27924,27925</link.rule.ids></links><search><creatorcontrib>Albertini, Claudia</creatorcontrib><creatorcontrib>Brodmann, Markus</creatorcontrib><title>A bound on certain local cohomology modules and application to ample divisors</title><title>Nagoya mathematical journal</title><addtitle>Nagoya Mathematical Journal</addtitle><description>We consider a positively graded noetherian domain R = ⊕n∈No
Rn
for which R0
is essentially of finite type over a perfect field K of positive characteristic and we assume that the generic fibre of the natural morphism π: Y = Proj(R) → Y
0 = Spec(R
0) is geometrically connected, geometrically normal and of dimension > 1. Then we give bounds on the “ranks” of the n-th homogeneous part H
2(R)n of the second local cohomology module of R with respect to R
+:= ⊕m>0
Rm
for n < 0. If Y is in addition normal, we shall see that the R
0-modules H
2
R
+ (R)n
are torsion-free for all n < 0 and in this case our bounds on the ranks furnish a vanishing result. From these results we get bounds on the first cohomology of ample invertible sheaves in positive characteristic.</description><subject>13D45</subject><subject>14B15</subject><issn>0027-7630</issn><issn>2152-6842</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><recordid>eNp9kM1KxDAUhYMoOI4-gLu8QDU3TdN25zD4ByMudNYlTdIxJW1K0grz9qZMcSN4NwfuPd-BexC6BXIHBPL7D0JonvOUzJOXND1DKwoZTXjB6Dlazedkvl-iqxDaaCrSMl2htw2u3dQr7HostR-F6bF1Ulgs3ZfrnHWHI-6cmqwOWESfGAZrpBhNBEaHRTdYjZX5NsH5cI0uGmGDvll0jfZPj5_bl2T3_vy63ewSyYCPSa2ygpFMZRnTRFEuVCN1qXlNChBlnUPJCtC8AVY2mnCVSU1IwxUQEadW6Ro9nHIH71otRz1Ja1Q1eNMJf6ycMNV2v1u2i_RdWwEA4ylwSmMEnCKkdyF43fzSQKq50upPpZFJF0Z0tTfqoKvWTb6Pr_5D_QC3HHpD</recordid><startdate>20010901</startdate><enddate>20010901</enddate><creator>Albertini, Claudia</creator><creator>Brodmann, Markus</creator><general>Cambridge University Press</general><general>Duke University Press</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20010901</creationdate><title>A bound on certain local cohomology modules and application to ample divisors</title><author>Albertini, Claudia ; Brodmann, Markus</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c416t-bd58405d554e0d26adfce9e6b081a9b719481e6f149fe06d5ce00f6d10aaaabd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>13D45</topic><topic>14B15</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Albertini, Claudia</creatorcontrib><creatorcontrib>Brodmann, Markus</creatorcontrib><collection>CrossRef</collection><jtitle>Nagoya mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Albertini, Claudia</au><au>Brodmann, Markus</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A bound on certain local cohomology modules and application to ample divisors</atitle><jtitle>Nagoya mathematical journal</jtitle><addtitle>Nagoya Mathematical Journal</addtitle><date>2001-09-01</date><risdate>2001</risdate><volume>163</volume><spage>87</spage><epage>106</epage><pages>87-106</pages><issn>0027-7630</issn><eissn>2152-6842</eissn><abstract>We consider a positively graded noetherian domain R = ⊕n∈No
Rn
for which R0
is essentially of finite type over a perfect field K of positive characteristic and we assume that the generic fibre of the natural morphism π: Y = Proj(R) → Y
0 = Spec(R
0) is geometrically connected, geometrically normal and of dimension > 1. Then we give bounds on the “ranks” of the n-th homogeneous part H
2(R)n of the second local cohomology module of R with respect to R
+:= ⊕m>0
Rm
for n < 0. If Y is in addition normal, we shall see that the R
0-modules H
2
R
+ (R)n
are torsion-free for all n < 0 and in this case our bounds on the ranks furnish a vanishing result. From these results we get bounds on the first cohomology of ample invertible sheaves in positive characteristic.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S0027763000007923</doi><tpages>20</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0027-7630 |
| ispartof | Nagoya mathematical journal, 2001-09, Vol.163, p.87-106 |
| issn | 0027-7630 2152-6842 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_nmj_1114631622 |
| source | Project Euclid |
| subjects | 13D45 14B15 |
| title | A bound on certain local cohomology modules and application to ample divisors |
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