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| | 004 |
 | | Let $\phi_1,\dots,\phi_\tau$ be a minimal set of generators for $M(f)$ over $\OYy$ with $\phi_i$ homogeneous of weight $w_{\phi_i}$ for all $i$.\newline Then $f$ has a symmetric discriminant matrix $A=(a_{ij})_{i,j}$ with respect to these generators, such that $a_{ij}$ is homogeneous in $\OYy$ of weight $2(d+d'-w) - w_{\phi_i} - w_{\phi_j}$ for all $i,j$. |
| | For any set of $\OYy$-generators of $M(f)$ there is a square matrix with entries in $\OYy$ whose columns span the module of relations among the generators minimally. |
| | In fact, if $\phi_1,\dots,\phi_k$ is a set of generators, then there exist an invertible $k\times k$-matrix $C$ with entries $C_{ij}\in \OYy$, such that with $\phi'_j=\sum_{i=1}^k C_{ij}\phi_i$ for $j=1,\dots,k$, then $\phi'_{\tau+1}=\dots=\phi'_k=0$ in $M(f)$ while $\phi'_1,\dots,\phi'_\tau$ constitute a minimal set of generators. |
| home.imf.au.dk /esn/preprints/004 (11725 words) |
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