What are monomial singularities?

Jun 25, 2014 ... Abstract. This is a general talk in front of specialists on computational dif- ferential algebra. Monomials play a significant role in most ... Apr 29, 2021 ... That's just the definition of a monomial. It is a product of variables. A binomial is defined as the sum of two monomials, so as a, b are ... Jan 31, 2022 ... I decided to formalize this definition and make it more rigorous by defining a monomial as a polynomial such that all the coefficients except one are zero. Let J ⊂ R a monomial ideal minimally generated by monomials. µ1,...,µr . For all subset σ ⊂ {1,...,r} we define the monomial. µ(J,σ) := lcm(µi |i ∈ σ) ∈ R ... Mar 12, 2025 ... When dividing monomials, we need to remember our exponent rules, specifically the rule xmxn=xm−n . This means that when bases raised to ... For a matroid M and rank r, we associate a monomial ideal (a monomial variant of the Orlik–Solomon ideal) to the set of flats of M of rank at most r. In ... Jan 9, 2024 ... A monomial is a mathematical expression in algebra that consists of a single term. Unlike other algebraic expressions that might have multiple terms separated ... Apr 3, 2024 ... ... monomial algebras, and aim to understand what the Auslander-Gorenstein property means in these settings. First, we will try to find a ... Definition: Monomial. A monomial is a single-term algebraic expression that is the product of constants and variables, where the variables only have nonnegative ... Abstract. We show that for every r ∈ Z>0 there exist monomial ideals generated in degree two, with linear syzygies, and regularity of the quotient equal to ...