Local Negativity of Surfaces With Non-Negative Kodaira Dimension and Transversal Configurations of Curves

Laface, Roberto; Pokora, Piotr

doi:10.1017/s0017089518000575

Cited by 3 publications

(4 citation statements)

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“…The Harbourne constants for line arrangements on X were first studied in [18]. The bounds obtained there were generalized in [15]. By [15,Theorem 3.2], the Harbourne constants of line arrangements C on X satisfy…”

Section: Introductionmentioning

confidence: 99%

“…The bounds obtained there were generalized in [15]. By [15,Theorem 3.2], the Harbourne constants of line arrangements C on X satisfy…”

Section: Introductionmentioning

confidence: 99%

“…The bounds on Harbourne constants were given in terms of the number of curves and the second Chern class of X. This bound was generalized to surfaces with non-negative Kodaira dimension in [15].…”

Section: Introductionmentioning

confidence: 99%

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Bounded negativity and Harbourne constants on ruled surfaces

Hanumanthu

Subramaniam

2020

manuscripta math.

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Let X be a smooth projective surface and let C be an arrangement of curves on X. The Harbourne constant of C was defined as a way to investigate the occurrence of curves of negative self-intersection on blow ups of X. This is related to the bounded negativity conjecture which predicts that the self-intersection number of all reduced curves on a surface is bounded below by a constant. We consider a geometrically ruled surface X over a smooth curve and give lower bounds for the Harbourne constants of transversal arrangements of curves on X. We also define a global Harbourne constant as the infimum of Harbourne constants for arrangements of a specific type and give a lower bound for it.

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Section: Introductionmentioning

confidence: 99%

“…The bounds obtained there were generalized in [15]. By [15,Theorem 3.2], the Harbourne constants of line arrangements C on X satisfy…”

Section: Introductionmentioning

confidence: 99%

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Bounded negativity and Harbourne constants on ruled surfaces

Hanumanthu

Subramaniam

2020

manuscripta math.

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“…This has paved the way to the study of the BNC from the point of view of configurations of curves via the notion of H-constant [2]. The H-constant is an asymptotic invariant that has the potential of studying the BNC on all blow-ups of a given algebraic surface at all possible configurations of points on it simultaneously, see for instance [2,8,9,18,19,15].…”

Section: Introductionmentioning

confidence: 99%

Towards the weighted Bounded Negativity Conjecture for blow-ups of algebraic surfaces

Laface

Pokora

2019

manuscripta math.

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In the present paper we focus on a weighted version of the Bounded Negativity Conjecture, which predicts that for every smooth projective surface in characteristic zero the self-intersection numbers of reduced and irreducible curves are bounded from below by a function depending on the intesection of curve with an arbitrary big and nef line bundle that is positive on the curve. We gather evidence for this conjecture by showing various bounds on the self-intersection number of curves in an algebraic surface. We focus our attention on blow-ups of algebraic surfaces, which have so far been neglected.

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