Cotangent cohomology of quadratic monomial ideals
Amin Nematbakhsh
TL;DR
This paper investigates the deformation theory of quadratic monomial ideals by computing their first cotangent cohomology module and providing criteria for the vanishing of the second, advancing understanding of their algebraic properties.
Contribution
It introduces explicit computations of cotangent cohomology for quadratic monomial ideals and establishes conditions for the vanishing of higher cohomology modules.
Findings
Computed the first cotangent cohomology module for quadratic monomial ideals
Provided a criterion for the vanishing of the second cotangent cohomology module
Enhanced understanding of deformation theory for these algebraic structures
Abstract
We study the deformation theory of quotients of polynomial rings by quadratic monomial ideals. More precisely we compute the first cotangent cohomology module of such rings. We also give a criterion for vanishing of second cotangent cohomology module.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory