A structure theorem for unions of complete intersections
Alfio Ragusa, Giuseppe Zappala
TL;DR
This paper establishes a structure theorem for unions of two complete intersections of codimension 2 that are arithmetically Cohen-Macaulay, enabling better understanding of their Hilbert functions and graded Betti numbers.
Contribution
It introduces a new structure theorem connecting almost complete intersections, arithmetically Gorenstein schemes, and unions of complete intersections.
Findings
Provides a formula for Hilbert functions of such unions
Determines graded Betti numbers for these schemes
Links various classes of schemes through a unifying structure
Abstract
Using the connections among almost complete intersection schemes, arithmetically Gorenstein schemes and schemes that are union of complete intersections we give a structure theorem for arithmetically Cohen-Macaulay union of two complete intersections of codimension We apply the results for computing Hilbert functions and graded Betti numbers for such schemes.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Advanced Combinatorial Mathematics