The Aluffi Algebra and Linearity Condition

Authors
Abbas Nasrollah Nejad 1
Parisa Solhi 2
1 Institute for Advanced Studies in Basic Sciences (IASBS) 444 Prof. Yousef Sobouti Blvd., Zanjan 45137-66731, Iran
2 Mohaghegh َArdebili Universit
Abstract
The Aluffi algebra is an algebraic version of characteristic cycles in intersection theory which is an intermediate graded algebra between the symmetric algebra (naive blowup) and the Rees algebra (blowup). Let R be a commutative Noetherian ring and J ⊂I ideals of R. We say that J ⊂I satisfy linearity condition if the Aluffi algebra of I/J is isomorphic with the symmetric algebra. In this paper, we present the necessary and sufficient conditions for satisfying linearity condition. We give classes of ideals J ⊂I which satisfy linearity condition. We prove that if J is a complete intersection ideal contained in I, then J ⊂I satisfy linearity condition if and only if the ideal I is of linear type.
Keywords
Aluffi Algebra
Blowup algebra
Singularity
Ideal of linear type
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Mathematical Research
Volume 8, Issue 4 - Serial Number 23
Autumn 2022
Pages 137-150