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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.

1 vote
0 answers
132 views

Degrees of polynomials defining a Jacobian of maximal rank on a variety

Let $f_1,\ldots,f_{n-k} \in \mathbb{R}[x_1,\ldots,x_n]$ be polynomials of degree at most $d$ defining an algebraic set $A \subseteq \mathbb{C}^n$ which contains an irreducible component $V \subseteq A …
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  • 121
11 votes
1 answer
859 views

Degrees of generators of radical ideals

Let $I \subseteq \mathbb{C}[x_1,\ldots,x_n]$ be an ideal generated by polynomials $f_1,\ldots,f_r$ of degree at most $d$. Is it possible to generate the radical $\sqrt{I}$ of this ideal with polynomia …
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  • 121