A SYMBOLIC POWER OF THE IDEAL OF A STANDARD k-CONFIGURATION IN P2
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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.
Abstract
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.
참고문헌 (9)
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