Smoothing and normalizing a singular curve
0
If we have a singular curve for example nodal curve then we can define its normalization.
I read somewhere we have also smoothing a singular curve
Does anyone know the definition or any references?
algebraic-geometry curves
asked Nov 25 at 15:05
Jigar Famil
63
|
show 1 more comment
0
If we have a singular curve for example nodal curve then we can define its normalization.
I read somewhere we have also smoothing a singular curve
Does anyone know the definition or any references?
algebraic-geometry curves
asked Nov 25 at 15:05
Jigar Famil
63
For curves, normalization is a resolution of singularities.
– Samir Canning
Nov 25 at 16:44
I know about normalization.I want to know what we mean by smoothing?
– Jigar Famil
Nov 25 at 17:27
You should specify in your question more about what you know. It was unclear whether you knew that the normalization of a curve is smooth. A smoothing result is usually a statement about families of curves, not just a fixed curve, that tells you the codimension of the locus of singular fibers of the family.
– Samir Canning
Nov 25 at 18:15
Would you please introduce some references for such smoothing results?
– Jigar Famil
Nov 25 at 19:09
link.springer.com/chapter/10.1007%2FBFb0074998. Here’s one where a bit of the history is explained in the introduction.
– Samir Canning
Nov 25 at 20:00
|
show 1 more comment
0
0
0
If we have a singular curve for example nodal curve then we can define its normalization.
I read somewhere we have also smoothing a singular curve
Does anyone know the definition or any references?
algebraic-geometry curves
asked Nov 25 at 15:05
Jigar Famil
63
If we have a singular curve for example nodal curve then we can define its normalization.
I read somewhere we have also smoothing a singular curve
Does anyone know the definition or any references?
algebraic-geometry curves
algebraic-geometry curves
asked Nov 25 at 15:05
Jigar Famil
63
asked Nov 25 at 15:05
Jigar Famil
63
edited Nov 25 at 15:14
asked Nov 25 at 15:05
Jigar Famil
63
asked Nov 25 at 15:05
Jigar Famil
63
asked Nov 25 at 15:05
Jigar Famil
63
63
For curves, normalization is a resolution of singularities.
– Samir Canning
Nov 25 at 16:44
I know about normalization.I want to know what we mean by smoothing?
– Jigar Famil
Nov 25 at 17:27
You should specify in your question more about what you know. It was unclear whether you knew that the normalization of a curve is smooth. A smoothing result is usually a statement about families of curves, not just a fixed curve, that tells you the codimension of the locus of singular fibers of the family.
– Samir Canning
Nov 25 at 18:15
Would you please introduce some references for such smoothing results?
– Jigar Famil
Nov 25 at 19:09
link.springer.com/chapter/10.1007%2FBFb0074998. Here’s one where a bit of the history is explained in the introduction.
– Samir Canning
Nov 25 at 20:00
|
show 1 more comment
For curves, normalization is a resolution of singularities.
– Samir Canning
Nov 25 at 16:44
I know about normalization.I want to know what we mean by smoothing?
– Jigar Famil
Nov 25 at 17:27
You should specify in your question more about what you know. It was unclear whether you knew that the normalization of a curve is smooth. A smoothing result is usually a statement about families of curves, not just a fixed curve, that tells you the codimension of the locus of singular fibers of the family.
– Samir Canning
Nov 25 at 18:15
Would you please introduce some references for such smoothing results?
– Jigar Famil
Nov 25 at 19:09
link.springer.com/chapter/10.1007%2FBFb0074998. Here’s one where a bit of the history is explained in the introduction.
– Samir Canning
Nov 25 at 20:00
For curves, normalization is a resolution of singularities.
– Samir Canning
Nov 25 at 16:44
For curves, normalization is a resolution of singularities.
– Samir Canning
Nov 25 at 16:44
I know about normalization.I want to know what we mean by smoothing?
– Jigar Famil
Nov 25 at 17:27
I know about normalization.I want to know what we mean by smoothing?
– Jigar Famil
Nov 25 at 17:27
You should specify in your question more about what you know. It was unclear whether you knew that the normalization of a curve is smooth. A smoothing result is usually a statement about families of curves, not just a fixed curve, that tells you the codimension of the locus of singular fibers of the family.
– Samir Canning
Nov 25 at 18:15
You should specify in your question more about what you know. It was unclear whether you knew that the normalization of a curve is smooth. A smoothing result is usually a statement about families of curves, not just a fixed curve, that tells you the codimension of the locus of singular fibers of the family.
– Samir Canning
Nov 25 at 18:15
Would you please introduce some references for such smoothing results?
– Jigar Famil
Nov 25 at 19:09
Would you please introduce some references for such smoothing results?
– Jigar Famil
Nov 25 at 19:09
link.springer.com/chapter/10.1007%2FBFb0074998. Here’s one where a bit of the history is explained in the introduction.
– Samir Canning
Nov 25 at 20:00
link.springer.com/chapter/10.1007%2FBFb0074998. Here’s one where a bit of the history is explained in the introduction.
– Samir Canning
Nov 25 at 20:00
|
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For curves, normalization is a resolution of singularities.
– Samir Canning
Nov 25 at 16:44
I know about normalization.I want to know what we mean by smoothing?
– Jigar Famil
Nov 25 at 17:27
You should specify in your question more about what you know. It was unclear whether you knew that the normalization of a curve is smooth. A smoothing result is usually a statement about families of curves, not just a fixed curve, that tells you the codimension of the locus of singular fibers of the family.
– Samir Canning
Nov 25 at 18:15
Would you please introduce some references for such smoothing results?
– Jigar Famil
Nov 25 at 19:09
link.springer.com/chapter/10.1007%2FBFb0074998. Here’s one where a bit of the history is explained in the introduction.
– Samir Canning
Nov 25 at 20:00