On Hilbert polynomial of certain determinantal ideals
Let X=(Xij) be an m(1) by m(2) matrix whose entries Xij, 1≤i≤m(1), 1≤j≤m(2); are indeterminates over a field K. Let K[X] be the polynomial ring in these m(1)m(2) variables over K. A part of the second fundamental theorem of Invariant Theory says that the ideal I[p+1] in K[X], generated by (p+1) by (...
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| Format: | Article |
| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171291000157 |
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| _version_ | 1832548613346033664 |
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| author | Shrinivas G. Udpikar |
| author_facet | Shrinivas G. Udpikar |
| author_sort | Shrinivas G. Udpikar |
| collection | DOAJ |
| description | Let X=(Xij) be an m(1) by m(2) matrix whose entries Xij, 1≤i≤m(1),
1≤j≤m(2); are indeterminates over a field K. Let K[X] be the polynomial ring in
these m(1)m(2) variables over K. A part of the second fundamental theorem of
Invariant Theory says that the ideal I[p+1] in K[X], generated by (p+1) by (p+1)
minors of X is prime. More generally in [1], Abhyankar defines an ideal I[p+a] in
K[X], generated by different size minors of X and not only proves its primeness but
also calculates the Hilbert function as well as the Hilbert polynomial of this
ideal. The said Hilbert polynomial is completely determined by certain integer valued
functions FD(m,p,a). In this paper we prove some important properties of these
integer valued functions. |
| format | Article |
| id | doaj-art-78cde478897542a1a63105ae77e4bffc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-78cde478897542a1a63105ae77e4bffc2025-02-03T06:13:39ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114115516210.1155/S0161171291000157On Hilbert polynomial of certain determinantal idealsShrinivas G. Udpikar0Department of Mathematics, S.P. College, Pune 411030, IndiaLet X=(Xij) be an m(1) by m(2) matrix whose entries Xij, 1≤i≤m(1), 1≤j≤m(2); are indeterminates over a field K. Let K[X] be the polynomial ring in these m(1)m(2) variables over K. A part of the second fundamental theorem of Invariant Theory says that the ideal I[p+1] in K[X], generated by (p+1) by (p+1) minors of X is prime. More generally in [1], Abhyankar defines an ideal I[p+a] in K[X], generated by different size minors of X and not only proves its primeness but also calculates the Hilbert function as well as the Hilbert polynomial of this ideal. The said Hilbert polynomial is completely determined by certain integer valued functions FD(m,p,a). In this paper we prove some important properties of these integer valued functions.http://dx.doi.org/10.1155/S0161171291000157standard bi-tableauxmonomials in minorsHilbert polynomial arithmetic genusirreducible varietyrecursive formula. |
| spellingShingle | Shrinivas G. Udpikar On Hilbert polynomial of certain determinantal ideals International Journal of Mathematics and Mathematical Sciences standard bi-tableaux monomials in minors Hilbert polynomial arithmetic genus irreducible variety recursive formula. |
| title | On Hilbert polynomial of certain determinantal ideals |
| title_full | On Hilbert polynomial of certain determinantal ideals |
| title_fullStr | On Hilbert polynomial of certain determinantal ideals |
| title_full_unstemmed | On Hilbert polynomial of certain determinantal ideals |
| title_short | On Hilbert polynomial of certain determinantal ideals |
| title_sort | on hilbert polynomial of certain determinantal ideals |
| topic | standard bi-tableaux monomials in minors Hilbert polynomial arithmetic genus irreducible variety recursive formula. |
| url | http://dx.doi.org/10.1155/S0161171291000157 |
| work_keys_str_mv | AT shrinivasgudpikar onhilbertpolynomialofcertaindeterminantalideals |