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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000157 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |