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43 views

Does this proof that the resultant provides an upper bound for intersection multiplicity look correct?

Let $f,g \in \mathbb{C}[x,y]$ such that $f(0,0)=g(0,0)=0$ and the varieties $V(f)$ and $V(g)$ are both smooth at $(0,0)$ such that the tangent line of $V(f)$ and $V(g)$ is not the $y$ axis. Let ...
2
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72 views

First order logic in polynomial equations

Have you ever wondered which points on a conic are the intersections of tangent lines of another surface through the origin? More generally, which points on a shape hold some specified relation to all ...
2
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0answers
83 views

How to tell if an ideal is absolutely prime

Consider the ideal $I=(ag-ec-1,ah+bg-cf-de)$ of $R=K[a,b,c,d,e,f,g,h]$. Is $I$ prime when $K=\overline{\mathbb{F}}_2$ is the algebraic closure of a field of 2 elements? Can computers answer this ...