Computation Initial Degree and Waldschmidt Constant for Sets of Small Number of Multiple Points

https://doi.org/10.31130/ud-jst.2023.098ICT
Tóm tắt: 37 | PDF: 100

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Author

  • Nguyen Chanh Tu
    The University of Danang - University of Science and Technology

Từ khóa:

Waldschmidt constant
initial degree
zero-dimensional scheme
fat points
path problem

Tóm tắt

Waldschmidt constant is firstly introduced by Waldschmidt in 1975. Since then, many results of this constant was achieved mostly about finding lower bounds. That is recently one of active, fascinating and important topics. However, computation of Waldschmidt constant or the initial degree is very hard in general, even for cases of small numbers of points  in the projective plane. Recently, the constants were computed for certain sets of points with one, two and three supporting lines. The paper shows values of the initial degree and Waldschmidt constant for sets with at most 6 points in all configurations in projective plane. These constants represent the complexity of optimal solutions in repeated path problems that have many applications in computer science, informatics theory and telecommunications.

Tài liệu tham khảo

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Jun 30, 2023
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Cách trích dẫn
Tu, N. C. “Computation Initial Degree and Waldschmidt Constant for Sets of Small Number of Multiple Points”. Tạp Chí Khoa học Và Công nghệ - Đại học Đà Nẵng, vol 21, số p.h 6.2, Tháng Sáu 2023, tr 21-24, doi:10.31130/ud-jst.2023.098ICT.

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