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A Groebner basis for the 2 [times] 2 determinantal ideal mod t [sup] 2
Košir, Tomaž, 1962- ; Sethuraman, B. A.
V članku avtorja nadaljujeta študij posplošenih determinantnih raznoterosti. To so raznoterosti skupnih ničel vseh koeficientov pri potencah ▫$t$▫ v vseh ▫$r \times r$▫ minorjih generične ▫$m\times ...n$▫ matrike nad kolobarjem polinomov ▫$F[t]/(t^k)$▫. V tem članku se posvetita primeru, ko je ▫$r=k=2$▫ in poiščeta Groebnerjevo bazo za ideal generiran z vsemi omenjenimi koeficienti. Pripadajača raznoterost predstavlja ravno tangentni sveženj za klasično determinantno raznoterost. S pomočjo teh Groebnerjevih baz so opisane vse komponente vseh posplošenih determinantnih raznoterosti za primer ▫$k=4$▫. Komponente za primera ▫$k=2$▫ in ▫$k=3$▫ so podane že v predhodnem članku [T. Košir, B.A. Sethuraman, Determinantal varieties over truncated polynomial rings, J. Pure Appl. Algebra 195 (2005) 75-95].
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