International Journal of Engineering Science and Applied Mathematics (IJESAM)

KLEIMAN'S CRITERION AND THE GEOMETRY OF AMPLE INVERTIBLE SHEAVES ON EXCEPTIONAL LOCI

Authors

  • Eleni Maria Koutoupis Aristotle University of Thessaloniki, Greece.
  • Nour Al-Din Hassan Al-Sayed University of Damascus, Syria, U.S.A.

Abstract

This paper explores the resolution of XXX-dimensional YYY-singularities by focusing on the exceptional locus E\mathcal{E}E, which consists of irreducible components Ei\mathcal{E}_iEi that are isomorphic to Pn\mathbb{P}^nPn. These components are studied in the context of invertible sheaves, with an emphasis on determining their ampleness. Utilizing Kleiman's Criterion (1966), the study establishes the necessary and sufficient conditions for ampleness of these sheaves. The results provide a comprehensive understanding of the geometric properties of the exceptional locus, contributing to the broader field of YYY-singularities and their resolutions. This investigation not only clarifies the conditions under which the sheaves are ample but also enhances the theoretical framework surrounding singularity resolution

Keywords:

Y-Singularities, Exceptional Locus, Ampleness, Kleiman's Criterion, Invertible Sheaves

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Published

2024-07-26

DOI:

https://doi.org/10.5281/zenodo.12923372

Issue

Vol. 15 No. 7 (2024): july

Section

Articles

How to Cite

Koutoupis , E. M., & Al-Sayed, N. A.-D. H. (2024). KLEIMAN’S CRITERION AND THE GEOMETRY OF AMPLE INVERTIBLE SHEAVES ON EXCEPTIONAL LOCI. International Journal of Engineering Science and Applied Mathematics (IJESAM), 15(7), 1–7. https://doi.org/10.5281/zenodo.12923372

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Copyright (c) 2024 Eleni Maria Koutoupis , Nour Al-Din Hassan Al-Sayed

Creative Commons License

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

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