How vanishing set irreducibility affects homogeneous polynomials
$begingroup$
I am trying to gain some insight into how the irreducibilty/reducibility of the vanishing set of a homogeneous polynomial affects the composition of the polynomial itself, so I am looking for two distinct examples of a polynomial $ginmathbb{C}[x,y,z]$ where $g$ is degree 2 and homogeneous and contains the point $(0:0:1)$ with a multiplicity greater than 1 and such that the same point $(0:0:1)$ is contained in the vanishing set $mathbb{V}(f)subsetmathbb{CP}^2$.
For one example, I would like $mathbb{V}(f)$ to be reducible and for the other, it should be irreducible.
algebraic-geometry polynomials
asked Dec 13 '18 at 14:59
mathgeenmathgeen
224
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add a comment |
$begingroup$
I am trying to gain some insight into how the irreducibilty/reducibility of the vanishing set of a homogeneous polynomial affects the composition of the polynomial itself, so I am looking for two distinct examples of a polynomial $ginmathbb{C}[x,y,z]$ where $g$ is degree 2 and homogeneous and contains the point $(0:0:1)$ with a multiplicity greater than 1 and such that the same point $(0:0:1)$ is contained in the vanishing set $mathbb{V}(f)subsetmathbb{CP}^2$.
For one example, I would like $mathbb{V}(f)$ to be reducible and for the other, it should be irreducible.
algebraic-geometry polynomials
asked Dec 13 '18 at 14:59
mathgeenmathgeen
224
$endgroup$
add a comment |
$begingroup$
I am trying to gain some insight into how the irreducibilty/reducibility of the vanishing set of a homogeneous polynomial affects the composition of the polynomial itself, so I am looking for two distinct examples of a polynomial $ginmathbb{C}[x,y,z]$ where $g$ is degree 2 and homogeneous and contains the point $(0:0:1)$ with a multiplicity greater than 1 and such that the same point $(0:0:1)$ is contained in the vanishing set $mathbb{V}(f)subsetmathbb{CP}^2$.
For one example, I would like $mathbb{V}(f)$ to be reducible and for the other, it should be irreducible.
algebraic-geometry polynomials
asked Dec 13 '18 at 14:59
mathgeenmathgeen
224
$endgroup$
I am trying to gain some insight into how the irreducibilty/reducibility of the vanishing set of a homogeneous polynomial affects the composition of the polynomial itself, so I am looking for two distinct examples of a polynomial $ginmathbb{C}[x,y,z]$ where $g$ is degree 2 and homogeneous and contains the point $(0:0:1)$ with a multiplicity greater than 1 and such that the same point $(0:0:1)$ is contained in the vanishing set $mathbb{V}(f)subsetmathbb{CP}^2$.
For one example, I would like $mathbb{V}(f)$ to be reducible and for the other, it should be irreducible.
algebraic-geometry polynomials
algebraic-geometry polynomials
asked Dec 13 '18 at 14:59
mathgeenmathgeen
224
asked Dec 13 '18 at 14:59
mathgeenmathgeen
224
asked Dec 13 '18 at 14:59
mathgeenmathgeen
224
asked Dec 13 '18 at 14:59
mathgeenmathgeen
224
asked Dec 13 '18 at 14:59
mathgeenmathgeen
224
224
add a comment |
add a comment |
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