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A note on d-sequences and regular sequences of quadrics
Let K be a field and X , Y denote matrices such that the entries of X are either indeterminates over K or 0, not all zero, and the entries of Y are indeterminates over K which are different from those appearing in X . We consider the ideal I 1 ( X Y ) , which is the ideal generated by the homogeneou...
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| Published in: | Proceedings of the Indian Academy of Sciences. Mathematical sciences 2022-12, Vol.132 (2) |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-springer_journals_10_1007_s12044_022_00719_x3 |
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| container_issue | 2 |
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| container_title | Proceedings of the Indian Academy of Sciences. Mathematical sciences |
| container_volume | 132 |
| creator | Saha, Joydip Sengupta, Indranath Tripathi, Gaurab |
| description | Let
K
be a field and
X
,
Y
denote matrices such that the entries of
X
are either indeterminates over
K
or 0, not all zero, and the entries of
Y
are indeterminates over
K
which are different from those appearing in
X
. We consider the ideal
I
1
(
X
Y
)
, which is the ideal generated by the homogeneous polynomials of degree 2 given by the
1
×
1
minors of the matrix
XY
. We prove that
d
-sequences and regular sequences arise naturally as part of generators of
I
1
(
X
Y
)
for some special cases. We use this information to calculate the equations defining the Rees algebra of
I
1
(
X
Y
)
. |
| doi_str_mv | 10.1007/s12044-022-00719-x |
| format | article |
| fullrecord | <record><control><sourceid>springer</sourceid><recordid>TN_cdi_springer_journals_10_1007_s12044_022_00719_x</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1007_s12044_022_00719_x</sourcerecordid><originalsourceid>FETCH-springer_journals_10_1007_s12044_022_00719_x3</originalsourceid><addsrcrecordid>eNqdzk0KwjAQBeAgCNafC7jKBaKTpjZ2KaJ4APdDaNPSUhKbMeDxrT_g3tXw5vHgY2wtYSMB9JZkClkmIE3FGGUhHhOWQKGV0Pl-N2Nzog5AFpnKE6YP3Pm75d7xSpAdonWlJW5cxYNtYm8C_319zYdoqtCWtGTT2vRkV9-7YOp8uh4vgm6hdY0N2PkY3FihBHy58OPC0YVvFz7Uf6sncq1DVw</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A note on d-sequences and regular sequences of quadrics</title><source>Springer Nature</source><creator>Saha, Joydip ; Sengupta, Indranath ; Tripathi, Gaurab</creator><creatorcontrib>Saha, Joydip ; Sengupta, Indranath ; Tripathi, Gaurab</creatorcontrib><description>Let
K
be a field and
X
,
Y
denote matrices such that the entries of
X
are either indeterminates over
K
or 0, not all zero, and the entries of
Y
are indeterminates over
K
which are different from those appearing in
X
. We consider the ideal
I
1
(
X
Y
)
, which is the ideal generated by the homogeneous polynomials of degree 2 given by the
1
×
1
minors of the matrix
XY
. We prove that
d
-sequences and regular sequences arise naturally as part of generators of
I
1
(
X
Y
)
for some special cases. We use this information to calculate the equations defining the Rees algebra of
I
1
(
X
Y
)
.</description><identifier>EISSN: 0973-7685</identifier><identifier>DOI: 10.1007/s12044-022-00719-x</identifier><language>eng</language><publisher>New Delhi: Springer India</publisher><subject>Mathematics ; Mathematics and Statistics</subject><ispartof>Proceedings of the Indian Academy of Sciences. Mathematical sciences, 2022-12, Vol.132 (2)</ispartof><rights>Indian Academy of Sciences 2022</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-springer_journals_10_1007_s12044_022_00719_x3</cites><orcidid>0000-0003-0349-8222</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Saha, Joydip</creatorcontrib><creatorcontrib>Sengupta, Indranath</creatorcontrib><creatorcontrib>Tripathi, Gaurab</creatorcontrib><title>A note on d-sequences and regular sequences of quadrics</title><title>Proceedings of the Indian Academy of Sciences. Mathematical sciences</title><addtitle>Proc Math Sci</addtitle><description>Let
K
be a field and
X
,
Y
denote matrices such that the entries of
X
are either indeterminates over
K
or 0, not all zero, and the entries of
Y
are indeterminates over
K
which are different from those appearing in
X
. We consider the ideal
I
1
(
X
Y
)
, which is the ideal generated by the homogeneous polynomials of degree 2 given by the
1
×
1
minors of the matrix
XY
. We prove that
d
-sequences and regular sequences arise naturally as part of generators of
I
1
(
X
Y
)
for some special cases. We use this information to calculate the equations defining the Rees algebra of
I
1
(
X
Y
)
.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0973-7685</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNqdzk0KwjAQBeAgCNafC7jKBaKTpjZ2KaJ4APdDaNPSUhKbMeDxrT_g3tXw5vHgY2wtYSMB9JZkClkmIE3FGGUhHhOWQKGV0Pl-N2Nzog5AFpnKE6YP3Pm75d7xSpAdonWlJW5cxYNtYm8C_319zYdoqtCWtGTT2vRkV9-7YOp8uh4vgm6hdY0N2PkY3FihBHy58OPC0YVvFz7Uf6sncq1DVw</recordid><startdate>20221215</startdate><enddate>20221215</enddate><creator>Saha, Joydip</creator><creator>Sengupta, Indranath</creator><creator>Tripathi, Gaurab</creator><general>Springer India</general><scope/><orcidid>https://orcid.org/0000-0003-0349-8222</orcidid></search><sort><creationdate>20221215</creationdate><title>A note on d-sequences and regular sequences of quadrics</title><author>Saha, Joydip ; Sengupta, Indranath ; Tripathi, Gaurab</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-springer_journals_10_1007_s12044_022_00719_x3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Saha, Joydip</creatorcontrib><creatorcontrib>Sengupta, Indranath</creatorcontrib><creatorcontrib>Tripathi, Gaurab</creatorcontrib><jtitle>Proceedings of the Indian Academy of Sciences. Mathematical sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Saha, Joydip</au><au>Sengupta, Indranath</au><au>Tripathi, Gaurab</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A note on d-sequences and regular sequences of quadrics</atitle><jtitle>Proceedings of the Indian Academy of Sciences. Mathematical sciences</jtitle><stitle>Proc Math Sci</stitle><date>2022-12-15</date><risdate>2022</risdate><volume>132</volume><issue>2</issue><eissn>0973-7685</eissn><abstract>Let
K
be a field and
X
,
Y
denote matrices such that the entries of
X
are either indeterminates over
K
or 0, not all zero, and the entries of
Y
are indeterminates over
K
which are different from those appearing in
X
. We consider the ideal
I
1
(
X
Y
)
, which is the ideal generated by the homogeneous polynomials of degree 2 given by the
1
×
1
minors of the matrix
XY
. We prove that
d
-sequences and regular sequences arise naturally as part of generators of
I
1
(
X
Y
)
for some special cases. We use this information to calculate the equations defining the Rees algebra of
I
1
(
X
Y
)
.</abstract><cop>New Delhi</cop><pub>Springer India</pub><doi>10.1007/s12044-022-00719-x</doi><orcidid>https://orcid.org/0000-0003-0349-8222</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 0973-7685 |
| ispartof | Proceedings of the Indian Academy of Sciences. Mathematical sciences, 2022-12, Vol.132 (2) |
| issn | 0973-7685 |
| language | eng |
| recordid | cdi_springer_journals_10_1007_s12044_022_00719_x |
| source | Springer Nature |
| subjects | Mathematics Mathematics and Statistics |
| title | A note on d-sequences and regular sequences of quadrics |
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