GEOMETRIC PROPERTIES OF AMPLE INVERTIBLE SHEAVES ON EXCEPTIONAL LOCI

https://doi.org/10.5281/zenodo.12801351

Authors

  • Nikos Alexandros Papadopoulos Aristotle University of Thessaloniki, Greece
  • Maria Eleni Georgiou University of Damascus, Syria, U.S.A.

Keywords:

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

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

Published

2024-07-24

How to Cite

Nikos , A. P., & Maria , E. G. (2024). GEOMETRIC PROPERTIES OF AMPLE INVERTIBLE SHEAVES ON EXCEPTIONAL LOCI. International Journal of Interdisciplinary Research in Statistics, Mathematics and Engineering (IJIRSME), 11(3), 1–7. https://doi.org/10.5281/zenodo.12801351

Issue

Vol. 11 No. 3 (2024): July-September

Section

Articles
Copyright & Licensing

Copyright (c) 2024 International Journal of Interdisciplinary Research in Statistics, Mathematics and Engineering (IJIRSME)

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

References

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