Mathematics - Research News

The resultants of quadratic binomial complete intersections

 Mathematics - Research News
 02 June 2020
Tadahito Harima, Akihito Wachi, Junzo Watanabe. Source: Journal of Commutative Algebra, Volume 12, Number 2, 217--235.Abstract: We compute the resultants for quadratic binomial complete intersections. As an application we show that any quadratic binomial complete intersection can have the set of...

On the ideal generated by all squarefree monomials of a given degree

 Mathematics - Research News
 02 June 2020
Federico Galetto. Source: Journal of Commutative Algebra, Volume 12, Number 2, 199--215.Abstract: An explicit construction is given of a minimal free resolution of the ideal generated by all squarefree monomials of a given degree. The construction relies upon and exhibits the natural action of the...

On finitely stable domains, II

 Mathematics - Research News
 02 June 2020
Stefania Gabelli, Moshe Roitman. Source: Journal of Commutative Algebra, Volume 12, Number 2, 179--198.Abstract: Among other results, we prove the following: A locally Archimedean stable domain satisfies accp. A stable domain R is Archimedean if and only if every nonunit of R ...

Stability of polytropic filtration equation with variable exponents

 Mathematics - Research News
 16 May 2020
Huashui Zhan, Zhaosheng Feng. Source: Advances in Differential Equations, Volume 25, Number 5/6, 255--278.Abstract: We are concerned with the stability of polytropic filtration equation with variable exponents, when the degeneracy occurs on the boundary. The existence and the local integrability...

Initial ideals of Pfaffian ideals

 Mathematics - Research News
 13 May 2020
Colby Long. Source: Journal of Commutative Algebra, Volume 12, Number 1, 91--105.Abstract: We explore the relationship between secant ideals and initial ideals of [math] , the ideal of the Grassmannian, [math] . The [math] -secant of [math] is the ideal generated by the [math] subpfaffians of a...

Finite unions of overrings of an integral domain

 Mathematics - Research News
 13 May 2020
Christian Gottlieb. Source: Journal of Commutative Algebra, Volume 12, Number 1, 87--90.Abstract: Let [math] be an integral domain, and let [math] be overrings of [math] , where [math] is of the form [math] , where [math] for some prime ideals [math] , and where each [math] , [math] , is of the...

A Gröbner basis for the graph of the reciprocal plane

 Mathematics - Research News
 13 May 2020
Alex Fink, David E. Speyer, Alexander Woo. Source: Journal of Commutative Algebra, Volume 12, Number 1, 77--86.Abstract: Given the complement of a hyperplane arrangement, let [math] be the closure of the graph of the map inverting each of its defining linear forms. The characteristic polynomial...

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