The regularity index of n+4 double points in projective spaces P^n for n=2 and n=3
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Investigating the regularity index of fat point schemes in higher-dimensional projective spaces remains a challenging problem and often relies on explicit computations in lower-dimensional cases. Such results provide valuable evidence for understanding the general behavior of the regularity index and for formulating broader conjectures. In this paper, we completely determine the regularity index of a set of n+4 double points not lying on two lines in the projective space P^n for the two fundamental dimensions n=2 and n=3. More precisely, we establish explicit formulas for the regularity index in both cases. These results contribute to the study of fat point schemes and provide a foundation for future investigations in higher-dimensional projective spaces.
Tài liệu tham khảo
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