Minimal free resolutions for homogeneous ideals with Betti numbers $1,n,n,1$
Alfio Ragusa, Giuseppe Zappal\`a
TL;DR
This paper studies the structure of minimal free resolutions for a specific class of homogeneous ideals with a symmetric Betti number pattern, providing a detailed description of their graded Betti numbers.
Contribution
It offers a structure theorem for resolutions of generalized Gorenstein algebras of homological dimension three and describes their graded Betti numbers comprehensively.
Findings
Structure theorem for resolutions of these algebras
Complete description of graded Betti numbers in many cases
Insights into the algebraic properties of these ideals
Abstract
We investigate the standard generalized Gorenstein algebras of homological dimension three, giving a structure theorem for their resolutions. Moreover in many cases we are able to give a complete description of their graded Betti numbers.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory