The Representation Type of Determinantal Varieties
This work is entirely devoted to construct huge families of indecomposable arithmetically Cohen-Macaulay (resp. Ulrich) sheaves E of arbitrary high rank on a general standard (resp. linear) determinantal scheme X ⊂ ℙ n of codimension c ≥ 1, n − c ≥ 1 and defined by the maximal minors of a t × ( t +...
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| Veröffentlicht in: | Algebras and representation theory 2017-08, Vol.20 (4), p.1029-1059 |
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| container_title | Algebras and representation theory |
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| creator | Kleppe, Jan O. Miró-Roig, Rosa M. |
| description | This work is entirely devoted to construct huge families of indecomposable arithmetically Cohen-Macaulay (resp. Ulrich) sheaves
E
of arbitrary high rank on a general standard (resp. linear) determinantal scheme
X
⊂
ℙ
n
of codimension
c
≥ 1,
n
−
c
≥ 1 and defined by the maximal minors of a
t
× (
t
+
c
−1) homogeneous matrix
A
. The sheaves
E
are constructed as iterated extensions of sheaves of lower rank. As applications: (1) we prove that any general standard determinantal scheme
X
⊂
ℙ
n
is of wild representation type provided the degrees of the entries of the matrix
A
satisfy some weak numerical assumptions; and (2) we determine values of
t
,
n
and
n
−
c
for which a linear standard determinantal scheme
X
⊂
ℙ
n
is of wild representation type with respect to the much more restrictive category of its indecomposable Ulrich sheaves, i.e.
X
is of Ulrich wild representation type. |
| doi_str_mv | 10.1007/s10468-017-9673-4 |
| format | Article |
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E
of arbitrary high rank on a general standard (resp. linear) determinantal scheme
X
⊂
ℙ
n
of codimension
c
≥ 1,
n
−
c
≥ 1 and defined by the maximal minors of a
t
× (
t
+
c
−1) homogeneous matrix
A
. The sheaves
E
are constructed as iterated extensions of sheaves of lower rank. As applications: (1) we prove that any general standard determinantal scheme
X
⊂
ℙ
n
is of wild representation type provided the degrees of the entries of the matrix
A
satisfy some weak numerical assumptions; and (2) we determine values of
t
,
n
and
n
−
c
for which a linear standard determinantal scheme
X
⊂
ℙ
n
is of wild representation type with respect to the much more restrictive category of its indecomposable Ulrich sheaves, i.e.
X
is of Ulrich wild representation type.</description><identifier>ISSN: 1386-923X</identifier><identifier>EISSN: 1572-9079</identifier><identifier>DOI: 10.1007/s10468-017-9673-4</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Associative Rings and Algebras ; Commutative Rings and Algebras ; Mathematics ; Mathematics and Statistics ; Non-associative Rings and Algebras ; Sheaves</subject><ispartof>Algebras and representation theory, 2017-08, Vol.20 (4), p.1029-1059</ispartof><rights>Springer Science+Business Media Dordrecht 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-6476dc243bbb79beb5ea071b39bd890e3396a1b10b4c38ed0d13719de8d5747b3</citedby><cites>FETCH-LOGICAL-c316t-6476dc243bbb79beb5ea071b39bd890e3396a1b10b4c38ed0d13719de8d5747b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10468-017-9673-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10468-017-9673-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Kleppe, Jan O.</creatorcontrib><creatorcontrib>Miró-Roig, Rosa M.</creatorcontrib><title>The Representation Type of Determinantal Varieties</title><title>Algebras and representation theory</title><addtitle>Algebr Represent Theor</addtitle><description>This work is entirely devoted to construct huge families of indecomposable arithmetically Cohen-Macaulay (resp. Ulrich) sheaves
E
of arbitrary high rank on a general standard (resp. linear) determinantal scheme
X
⊂
ℙ
n
of codimension
c
≥ 1,
n
−
c
≥ 1 and defined by the maximal minors of a
t
× (
t
+
c
−1) homogeneous matrix
A
. The sheaves
E
are constructed as iterated extensions of sheaves of lower rank. As applications: (1) we prove that any general standard determinantal scheme
X
⊂
ℙ
n
is of wild representation type provided the degrees of the entries of the matrix
A
satisfy some weak numerical assumptions; and (2) we determine values of
t
,
n
and
n
−
c
for which a linear standard determinantal scheme
X
⊂
ℙ
n
is of wild representation type with respect to the much more restrictive category of its indecomposable Ulrich sheaves, i.e.
X
is of Ulrich wild representation type.</description><subject>Associative Rings and Algebras</subject><subject>Commutative Rings and Algebras</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Non-associative Rings and Algebras</subject><subject>Sheaves</subject><issn>1386-923X</issn><issn>1572-9079</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LxDAQhoMouK7-AG8Fz9GZJk2ao6yfsCBIFW8haWe1y25bk-5h_71Z6sGLpxmY530HHsYuEa4RQN9EBKlKDqi5UVpwecRmWOicG9DmOO2iVNzk4uOUncW4BgCjSpyxvPqi7JWGQJG60Y1t32XVfqCsX2V3NFLYtp1Lh0327kJLY0vxnJ2s3CbSxe-cs7eH-2rxxJcvj8-L2yWvBaqRK6lVU-dSeO-18eQLcqDRC-Ob0gAJYZRDj-BlLUpqoEGh0TRUNoWW2os5u5p6h9B_7yiOdt3vQpdeWjSotFGqUInCiapDH2OglR1Cu3VhbxHsQY2d1Nikxh7UWJky-ZSJie0-Kfxp_jf0A10mZcs</recordid><startdate>20170801</startdate><enddate>20170801</enddate><creator>Kleppe, Jan O.</creator><creator>Miró-Roig, Rosa M.</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170801</creationdate><title>The Representation Type of Determinantal Varieties</title><author>Kleppe, Jan O. ; Miró-Roig, Rosa M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-6476dc243bbb79beb5ea071b39bd890e3396a1b10b4c38ed0d13719de8d5747b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Associative Rings and Algebras</topic><topic>Commutative Rings and Algebras</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Non-associative Rings and Algebras</topic><topic>Sheaves</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kleppe, Jan O.</creatorcontrib><creatorcontrib>Miró-Roig, Rosa M.</creatorcontrib><collection>CrossRef</collection><jtitle>Algebras and representation theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kleppe, Jan O.</au><au>Miró-Roig, Rosa M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Representation Type of Determinantal Varieties</atitle><jtitle>Algebras and representation theory</jtitle><stitle>Algebr Represent Theor</stitle><date>2017-08-01</date><risdate>2017</risdate><volume>20</volume><issue>4</issue><spage>1029</spage><epage>1059</epage><pages>1029-1059</pages><issn>1386-923X</issn><eissn>1572-9079</eissn><abstract>This work is entirely devoted to construct huge families of indecomposable arithmetically Cohen-Macaulay (resp. Ulrich) sheaves
E
of arbitrary high rank on a general standard (resp. linear) determinantal scheme
X
⊂
ℙ
n
of codimension
c
≥ 1,
n
−
c
≥ 1 and defined by the maximal minors of a
t
× (
t
+
c
−1) homogeneous matrix
A
. The sheaves
E
are constructed as iterated extensions of sheaves of lower rank. As applications: (1) we prove that any general standard determinantal scheme
X
⊂
ℙ
n
is of wild representation type provided the degrees of the entries of the matrix
A
satisfy some weak numerical assumptions; and (2) we determine values of
t
,
n
and
n
−
c
for which a linear standard determinantal scheme
X
⊂
ℙ
n
is of wild representation type with respect to the much more restrictive category of its indecomposable Ulrich sheaves, i.e.
X
is of Ulrich wild representation type.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10468-017-9673-4</doi><tpages>31</tpages></addata></record> |
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| identifier | ISSN: 1386-923X |
| ispartof | Algebras and representation theory, 2017-08, Vol.20 (4), p.1029-1059 |
| issn | 1386-923X 1572-9079 |
| language | eng |
| recordid | cdi_proquest_journals_1916796656 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Associative Rings and Algebras Commutative Rings and Algebras Mathematics Mathematics and Statistics Non-associative Rings and Algebras Sheaves |
| title | The Representation Type of Determinantal Varieties |
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