## Kodai Mathematical Journal

### An algebraic approach to the regularity index of fat points in ${\bf P}^n$

Ngô Việt Trung

#### Article information

Source
Kodai Math. J., Volume 17, Number 3 (1994), 382-389.

Dates
First available in Project Euclid: 23 January 2006

https://projecteuclid.org/euclid.kmj/1138040029

Digital Object Identifier
doi:10.2996/kmj/1138040029

Mathematical Reviews number (MathSciNet)
MR1296905

Zentralblatt MATH identifier
0821.14030

#### Citation

Trung, Ngô Việt. An algebraic approach to the regularity index of fat points in ${\bf P}^n$. Kodai Math. J. 17 (1994), no. 3, 382--389. doi:10.2996/kmj/1138040029. https://projecteuclid.org/euclid.kmj/1138040029

#### References

• [1] J. Alexander, Singularites imposable enposition general a une hypersurface projective, Compos. Math. 68 (1988), 305-354.
• [2] M. V. Catalisano, Linear systems of plane curves through fixed "fat" points in P2, J. Algebr 142 (1991), 81-100.
• [3] M. V. Catalisano, N. V. Trung, and G. Valla, A sharp bound for the regularity index of fat point in general position, Proc. Amer. Math. Soc., to appear.
• [4] E. D. Davis and A. V. Geramita, The Hilbert function of a special class of 1-dimensional Cohen Macaulay graded algebras, The Curves Seminar at Queen's, Queen's Papers in Pure and Appl. Math. 67 (1984), l-29.
• [5] D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicity, J. Algebra 88 (1984), 89-133
• [6] W. Fulton, Algebraic Curves, Math. Lect. Note Series, Benjamin 1969
• [7] A. Gimigliano, Our thin knowledge on fat points, in: The Curve's Seminar at Queen's VI, Queen's Papers in Pure and Appl. Math. 83 (1989)
• [8] A. Gimigliano, Regularity of linear systems of plane curves, J. Algebra 124 (1989), 447-460
• [9] S. Greco, Remarks on the postulation of zero-dimensional subschemes of projective spaces, Math Ann 284 (1989), 343-351.
• [10] J. Harris, A bound on the geometric genus of projective varieties, Ann. Sc. Norm. Sup. Pisa Ser IV. 8 (1981), 35-68.
• [11] J. Harris (with the collaboration of D. Eisenbud), Curves in projective spaces, Les Presses d Universite de Montreal 1982.
• [12] A. Hirschowitz, La methode d'Horace pour lnterpolation a plusieurs variables, Manus. Math 50 (1985), 337-388.
• [13] A. Ooishi, Castelnuovo's regularity of graded rings and modules, Hiroshima Math. J. 12 (1982), 627-649
• [14] G. Paxia, On flat families of fat points, Proc. Amer. Math. Soc. 112 (1991), 19-23
• [15] J. Rathmann, The uniform position principle for curves in charcteristic p, Math. Ann. 27 (1987), 565-579.
• [16] B. Segre, Alcune question! su insiemi finiti di punti in geometria algebrica, Atti. Convergno Intern, di Torino 1961, 15-33.
• [17] R. Treger, On equations defining arithmetically Cohen-Macaulay schemes I, Math. Ann. 26 (1982), 141-153.
• [18] N. V. Trung and G. Valla, Degree bounds for the defining equations of arithmetically Cohen Macaulay curves, Math. Ann. 281 (1988), 209-218.
• [19] N. V. Trung and G. Valla, Upper bounds for the regularity index of fat points with unifor position property, Preprint.