The uniqueness of a fixed degree singular plane model
Abstract
Let
be the normalization of an integral degree
plane curve
. We prove that
has a unique
if
, where
is the conductor of
. Moreover,
is the unique plane model of
of degree at most
.
![X](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/02129bb861061d1a052c592e2dc6b383.png)
![d\ge 9](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/1ead0e23e104fdaae0a0b9e98487d0b5.png)
![Y](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/57cec4137b614c87cb4e24a3d003a3e0.png)
![X](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/02129bb861061d1a052c592e2dc6b383.png)
![g^2_d](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/bb5f3d5277a71e04530489c6616e18f6.png)
![h^1(\mathbb{P}^2,\mathcal{I}_Z(\lceil d/2\rceil -3))=0](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/2705a70cb43c52b16be9c249f056f780.png)
![Z](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/21c2e59531c8710156d34a3c30ac81d5.png)
![Y](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/57cec4137b614c87cb4e24a3d003a3e0.png)
![Y](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/57cec4137b614c87cb4e24a3d003a3e0.png)
![X](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/02129bb861061d1a052c592e2dc6b383.png)
![d](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/8277e0910d750195b448797616e091ad.png)
Keywords:
plane curve; uniqueness of a plane model
Full Text: PDF