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Ideal Containments Under Flat Extensions And Interpolation On Linear Systems In P2, Solomon Akesseh
Ideal Containments Under Flat Extensions And Interpolation On Linear Systems In P2, Solomon Akesseh
Department of Mathematics: Dissertations, Theses, and Student Research
Fat points and their ideals have stimulated a lot of research but this dissertation concerns itself with aspects of only two of them, broadly categorized here as, the ideal containments and polynomial interpolation problems.
Ein-Lazarsfeld-Smith and Hochster-Huneke cumulatively showed that for all ideals I in k[Pn], I(mn) ⊆ Im for all m ∈ N. Over the projective plane, we obtain I(4)< ⊆ I2. Huneke asked whether it was the case that I(3) ⊆ I2. Dumnicki, Szemberg and Tutaj-Gasinska show that if I is the saturated homogeneous radical ideal of the 12 …