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LOCAL NEGATIVITY OF SURFACES WITH NON-NEGATIVE KODAIRA DIMENSION AND TRANSVERSAL CONFIGURATIONS OF CURVES

Part of: Discrete geometry Singularities Cycles and subschemes Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  18 January 2019

ROBERTO LAFACE  and
PIOTR POKORA Open the ORCID record for PIOTR POKORA [Opens in a new window]
ROBERTO LAFACE
Affiliation:
Technische Universität München, Zentrum Mathematik—M11, Boltzmannstrasse 3, 85748 Garching bei München, Germany e-mail: [email protected]
PIOTR POKORA*
Affiliation:
Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany e-mail: [email protected]
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Abstract

We give a bound on the H-constants of configurations of smooth curves having transversal intersection points only on an algebraic surface of non-negative Kodaira dimension. We also study in detail configurations of lines on smooth complete intersections $X \subset \mathbb{P}_{\mathbb{C}}^{n + 2}$ of multi-degree d = (d1, …, dn), and we provide a sharp and uniform bound on their H-constants, which only depends on d.

MSC classification

Primary: 14C20: Divisors, linear systems, invertible sheaves
Secondary: 14J70: Hypersurfaces 52C35: Arrangements of points, flats, hyperplanes 32S22: Relations with arrangements of hyperplanes
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 1 , January 2020 , pp. 123 - 135
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019 

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Footnotes

Present address: Piotr Pokora, Institute of Mathematics of the Polish Academy of Sciences, Śniadeckich 8, PL-00-656 Warsaw, Poland

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