Geometry of the locus of polynomials of degree 4 with iterative roots
We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.
Remarks on the Nagata Conjecture
2000 Mathematics Subject Classification: 14C20, 14E25, 14J26. The famous Nagata Conjecture predicts the lowest degree of a plane curve passing with prescribed multiplicities through given points in general position. We explain how this conjecture extends naturally via multiple point Seshadri constants to ample line bundles on arbitrary surfaces. We show that if there exist curves of unpredictable low degree, then they must have equal multiplicities in all but possibly one of the given...
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