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In [4], the authors show that if X is a k-configuration in P2 of type (d1, . . . , ds) with ds > s 2, then HmX(mds−1) is the number of lines containing exactly ds-points of X for m 2. They also show that if X is a k-configuration in P2 of type (1, 2, . . . , s) with s 2, then HmX(mX − 1) is the number of lines containing exactly s-points in X for m s+1. In this paper, we explore a standard k-configuration in P2 and find that if X is a standard k-configuration in P2 of type (1, 2, . . . , s) with s 2, then HmX(mX − 1) = 3, which is the number of lines containing exactly s-points in X for m 2 instead of m s + 1.
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참고문헌 (9)
참고문헌 신청
C. Bocci / 2010 / Comparing powers and symbolic powers of ideals / J. Alge-braic Geom. 19(3):399~417
S. Cooper / 2011 / Combinatorial bounds on Hilbert functions of fat points in projective space / J. Pure Appl. Algebra 215:2165~2179
F. Galetto / The Symbolic Defect of an Ideal
F. Galetto / Distinguishing $\mathbb{k}$ -configurations
A.V. Geramita / 2013 / Star Configurations in $\mathbb{P}^n$ / J. Algebra 376:279~299
S. Cooper / 2011 / Combinatorial bounds on Hilbert functions of fat points in projective space / J. Pure Appl. Algebra 215:2165~2179
F. Galetto / The Symbolic Defect of an Ideal
F. Galetto / Distinguishing
A.V. Geramita / 2013 / Star Configurations in
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