The equations of almost complete intersections

Hong, Jooyoun; Simis, Aron; Vasconcelos, Wolmer V.

doi:10.1007/s00574-012-0009-z

Cited by 26 publications

(35 citation statements)

References 21 publications

(41 reference statements)

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“…In [12], F. Muiños and F. Planas-Vilanova recover this result by proving in addition that there is a unique defining equation of R(I ) of maximal degree. Also, their work recovers Theorem 2.3.3 in [19], for the case reduction number equal to 1 (see also [9]). For the relation between the reltype and the reduction number, see for example [10,11,16], among others.…”

Section: Introductionmentioning

confidence: 57%

On the Relation Type of Fiber Cone

Jayanthan

Nanduri

2015

Acta Math Vietnam

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In this article, we study the relation type of the fiber cone of certain special classes of ideals in Noetherian local rings. We show that in any Noetherian local ring, if deviation of I is 1, and depth(G(F L )) ≥ − 1, then the relation types of R(I ) and F L (I ) are equal. We also prove that for lexsegment ideals in K [x, y], where K is a field, the relation types of the fiber cone and the Rees algebra are equal.

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Section: Introductionmentioning

confidence: 57%

On the Relation Type of Fiber Cone

Jayanthan

Nanduri

2015

Acta Math Vietnam

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“…As a consequence, one has e 1 (I) = 1 2 (d 2 − d) = d 2 and deg(R/I) = d (see [4,Proposition 3.3]). It also follows that the reduction number of I is d − 1.…”

Section: Smentioning

confidence: 99%

The depth of the Rees algebra of three general binary forms

Burity

Simis

2019

Communications in Algebra

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One proves that the Rees algebra of an ideal generated by three general binary forms of same degree ≥ 5 has depth one. The proof hinges on the behavior of the Ratliff-Rush filtration for low powers of the ideal and on establishing that certain large matrices whose entries are quadratic forms have maximal rank. One also conjectures a shorter result that implies the main theorem of the paper.2010 Mathematics Subject Classification. 13A02, 13A30, 13C15, 13D02, 13D40.Plugging this back into the above equation, after canceling P x d , and after simplifying by y, one has P y 2 g 1 + Q x d−1 + y 2 Q g 2 − xyP g 2 + Rx d−2 + yRg 3 = 0.Again, plugging this back, canceling Q x d−1 , and simplifying by y yields P (yg 1 − xg 2 ) + Q (yg 2 − xg 3 ) + R (x d−2 + yg 3 ) = 0.

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“…By a known argument as in [5], one can show that the maximal minors of ψ are polynomial relations of the 5 original quadrics. Therefore, since dim k[I] = 3 the codimension of the ideal I 3 (ψ) is at most 2.…”

Section: Exceptionsmentioning

confidence: 99%

The Aluffi algebra of the Jacobian of points in projective space: Torsion-freeness

2016

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The algebra in the title has been introduced by P. Aluffi. Let J ⊂ I be ideals in the commutative ring R. The (embedded) Aluffi algebra of I on R/J is an intermediate graded algebra between the symmetric algebra and Rees Algebra of the ideal I/J over R/J. A pair of ideals has been dubbed an Aluffi torsion-free pair if the surjective map of the Aluffi algebra of I/J onto the Rees algebra of I/J is injective. In this paper we focus on the situation where J is the ideal of points in general linear position in projective space and I is its Jacobian ideal.

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The equations of almost complete intersections

Cited by 26 publications

References 21 publications

On the Relation Type of Fiber Cone

On the Relation Type of Fiber Cone

The depth of the Rees algebra of three general binary forms

The Aluffi algebra of the Jacobian of points in projective space: Torsion-freeness

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