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GEOMETRIC PROPERTIES OF AMPLE INVERTIBLE SHEAVES ON EXCEPTIONAL LOCI

Authors: Nikos, Alexandros Papadopoulos; Maria, Eleni Georgiou;

GEOMETRIC PROPERTIES OF AMPLE INVERTIBLE SHEAVES ON EXCEPTIONAL LOCI

Abstract

This paper addresses the resolution of X\mathcal{X}X-dimensional Y\mathcal{Y}Y-singularity, focusing on the exceptional locus E\mathcal{E}E, where E\mathcal{E}E comprises irreducible components Ei\mathcal{E}_iEi isomorphic to Pn\mathbb{P}^nPn. These components are examined as invertible sheaves. The study investigates the conditions under which these sheaves are ample, utilizing Kleiman's Criterion (Kleiman, 1966) as a foundational tool. By applying this criterion, we determine the necessary and sufficient conditions for ampleness, offering insights into the geometric properties of the exceptional locus and contributing to the broader understanding of Y\mathcal{Y}Y-singularities and their resolutions

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Keywords

Y\mathcal{Y}Y-singularity, Exceptional locus, Irreducible components, Invertible sheaves, Kleiman's Criterion

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average