Abstract
We simplify the Ciliberto and Miranda method (Ciliberto and Miranda, 2008) [4] to construct degenerations of C P 2 blown up in several points yielding lower bounds of the corresponding multi-point Seshadri constants. In particular we exploit an asymptotic result of (Eckl, 2008) [6] which allows us to check the non-specialty of much fewer linear systems on C P 2 . We obtain the lower bound 117 370 for the 10-point Seshadri constant on C P 2 .
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