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Towards bounded negativity of self-intersection on general blown-up projective planes. (English) Zbl 1245.14012
Summary: We address the problem of bounding from below the self-intersection of integral curves on the projective plane blown-up at general points. In particular, by applying classical deformation theory, we obtain the expected bound in the case of either high ramification or low multiplicity.

MSC:
14D15 Formal methods and deformations in algebraic geometry
14H50 Plane and space curves
14J26 Rational and ruled surfaces
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