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Bounded negativity, Harbourne constants ...
Pokora, Piotr...

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Bounded negativity, Harbourne constants and transversal arrangements of curves by Pokora, Piotr ( Author )
Lemonjar Open Access
N.A
07-02-2016
The Bounded Negativity Conjecture predicts that for every complex projective surface X there exists a number b(X) such that C2≥−b(X) holds for all reduced curves C⊂X. For birational surfaces f:Y→X there have been introduced certain invariants (Harbourne constants) relating to the effect the numbers b(X), b(Y) and the complexity of the map f. These invariants have been studied previously when f is the blowup of all singular points of an arrangement of lines in P2, of conics and of cubics. In the present note we extend these considerations to blowups of P2 at singular points of arrangements of curves of arbitrary degree d. We also considerably generalize and modify the approach witnessed so far and study transversal arrangements of sufficiently positive curves on arbitrary surfaces with the non-negative Kodaira dimension.
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Article
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1602.02379
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