# Tagged Questions

A monomial ideal in a polynomial ring is an ideal generated by monomials.

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### Vanishing ideal of a finite set of points does not have expected amount of cones in Gröbner fan

I am reading the paper A Gröbner fan method for biochemical network modeling. In Chapter 4.3 (i.stack.imgur.com/h2O8B.png) they calculate the vanishing ideal of some tuples (input points of Series 1-...
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### Primary decompositions of squares (products) of monomial ideals

Is there anything known about the relation between the primary decomposition of a monomial ideal $I$ and the primary decomposition of $I^2$? In other words, given the standard primary decomposition ...
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### Castelnuovo- Mumford regularity properties

Let $R=k[x_1,\ldots,x_n]$ be a graded ring and $S,T,U$ be monomials ideals. $reg(S)=max\{j-i \backslash \beta_{i,j}(S) \neq 0\}$. Assume $S+T=U$ prove \disprove : $reg(S+T^2) \leq reg(U^2)$. We can ...
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### Families of ideals with a given initial ideal

Assume a fintie set of monomials is given. Is there a way to find the family of ideals whose initial ideal (say w.r.t revlex order) is generated by that finite set? I'll appreciate any partial answer, ...
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### betti-numbers of Gin(I), generic initial ideal of $I$

here in the paper Ideals with Stable Betti Numbers there is a theorem that I can't uderstand it, both in details (which highlighted) and sketch of the proof of (b): can you help please? ...