Search results for "Points in ℙ1× ℙ1"

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The minimal free resolution of fat almost complete intersections in ℙ1 x ℙ1

2017

AbstractA current research theme is to compare symbolic powers of an ideal I with the regular powers of I. In this paper, we focus on the case where I = IX is an ideal deûning an almost complete intersection (ACI) set of points X in ℙ1 × ℙ1. In particular, we describe a minimal free bigraded resolution of a non-arithmetically Cohen-Macaulay (also non-homogeneous) set 𝒵 of fat points whose support is an ACI, generalizing an earlier result of Cooper et al. for homogeneous sets of triple points. We call 𝒵 a fat ACI.We also show that its symbolic and ordinary powers are equal, i.e, .

Current (mathematics)Ideal (set theory)General MathematicsPoints in ℙ1× ℙ1010102 general mathematicsComplete intersectionArithmetically Cohen-Macaulay; Points in ℙ1× ℙ1; Resolution; Symbolic powersSymbolic powers01 natural sciencesArithmetically Cohen-MacaulayCombinatoricsSet (abstract data type)Settore MAT/02 - AlgebraHomogeneous0103 physical sciencesArithmetically Cohen-Macaulay Points in ℙ1xℙ1 Resolution Symbolic powersSettore MAT/03 - Geometria010307 mathematical physics0101 mathematicsResolutionFocus (optics)Resolution (algebra)Mathematics
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