Results 31 to 40 of about 237,348 (199)
Degenerations of Monomial Ideals [PDF]
Mathematical Research Letters, 2004 In the paper under review the author describes the degenerations of monomial ideals in \(K[[x,y]]\) with \(\text{ Aut}(K[[x,y]])\)-orbit of dimension at most \(3\). In particular, she determines the monomial ideals that any power of \((x,y^4)\) can degenerate to and makes a conjecture about all the ideals that the powers of \((x,y^4)\) can degenerate ...
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Monomial difference ideals [PDF]
Proceedings of the American Mathematical Society, 2016 In this paper, basic properties of monomial difference ideals are studied. We prove the finitely generated property of well-mixed difference ideals generated by monomials. Furthermore, a finite prime decomposition of radical well-mixed monomial difference ideals is given.
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Families of finite sets in which no set is covered by the union of the others
Examples and Counterexamples, 2023 Let ℱ be a finite nonempty family of finite nonempty sets. We prove the following: (1) ℱ satisfies the condition of the title if and only if for every pair of distinct subfamilies {A1,…,Ar}, {B1,…,Bs}of ℱ, ⋃i=1rAi≠⋃i=1sBi.
Guillermo Alesandroni
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Free Resolutions Of Monomial Ideals [PDF]
, 2011 Let k be a field and S = k [x1 , . . . , xn ] a polynomial ring. This thesis considers the structure of minmial free resolutions of monomial ideals in S . In Chapter 3 we study reverse lex ideals, and compare their properties to those of lex ideals.
Biermann, Jennifer
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Multiplier ideals of monomial space curves
Proceedings of the American Mathematical Society, Series B, 2014 This paper presents a formula for the multiplier ideals of a monomial space curve. The formula is obtained from a careful choice of log resolution. We construct a toric blowup of affine space in such a way that a log resolution of
Howard M Thompson
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Blowups in tame monomial ideals [PDF]
, 2011 Tame monomial ideals are monomial ideals that render smooth blowups of affine n-space. We give a combinatorial description of tame ideals and discuss its applications in the following cases: a smoothing procedure proposed by Rosenberg, monomial building ...
D.B. Westra +3 more
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Extremal Betti Numbers of t-Spread Strongly Stable Ideals
Mathematics, 2019 Let K be a field and let S = K [ x 1 , ⋯ , x n ] be a polynomial ring over K. We analyze the extremal Betti numbers of special squarefree monomial ideals of S known as the t-spread strongly stable ideals, where t is an integer ≥ 1
Luca Amata, Marilena Crupi
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Minimal Systems of Binomial Generators for the Ideals of Certain Monomial Curves
Mathematics, 2021 Let a,b and n>1 be three positive integers such that a and ∑j=0n−1bj are relatively prime. In this paper, we prove that the toric ideal I associated to the submonoid of N generated by {∑j=0n−1bj}∪{∑j=0n−1bj+a∑j=0i−2bj∣i=2,…,n} is determinantal. Moreover,
Manuel B. Branco +2 more
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Monomial ideals of minimal depth
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013 Let S be a polynomial algebra over a field. We study classes of monomial ideals (as for example lexsegment ideals) of S having minimal depth. In particular, Stanley's conjecture holds for these ideals.
Ishaq Muhammad
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Communications in Algebra, 2000 We show how to lift any monomial ideal J in n variables to a saturated ideal I of the same codimension in n+t variables. We show that I has the same graded Betti numbers as J and we show how to obtain the matrices for the resolution of I. The cohomology of I is described.
Migliore, Juan C., Nagel, Uwe
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