Mixing
Normalization of varieties.
$begingroup$
In "E. Arbarello, M. Cornalba, P.A. Griffiths, J. Harris-
Geometry of Algebraic Curves Volume 1 ", page 246 is considered a morphism $f:X longrightarrow mathbb{P}^n$, where X is a quasiprojective variety. Then it is considered $Gamma$ be the closure of the graph of $f$ and denote by $widehat{Gamma}$ its normalization. Continuing, it is considered $F:widehat{Gamma} longrightarrow mathbb{P}^n$ be the induced morphism.
My questions are:
1) What is the normalization of $Gamma$?
2)What is the relationship between the two morphisms?
3)Where to read about what was done above, reference?
Thank you!
Happy New Year!
algebraic-geometry
asked Jan 1 at 20:37
ManoelManoel
922518
$endgroup$
add a comment |
$begingroup$
In "E. Arbarello, M. Cornalba, P.A. Griffiths, J. Harris-
Geometry of Algebraic Curves Volume 1 ", page 246 is considered a morphism $f:X longrightarrow mathbb{P}^n$, where X is a quasiprojective variety. Then it is considered $Gamma$ be the closure of the graph of $f$ and denote by $widehat{Gamma}$ its normalization. Continuing, it is considered $F:widehat{Gamma} longrightarrow mathbb{P}^n$ be the induced morphism.
My questions are:
1) What is the normalization of $Gamma$?
2)What is the relationship between the two morphisms?
3)Where to read about what was done above, reference?
Thank you!
Happy New Year!
algebraic-geometry
asked Jan 1 at 20:37
ManoelManoel
922518
$endgroup$
2
$begingroup$
Have you checked reference texts, Wikipedia or Stacksproject? If so, are there specific points you're confused about?
$endgroup$
– KReiser
Jan 1 at 20:40
$begingroup$
I checked Shafarevich. I could not clear the vision. The specific points are the questions I put.
$endgroup$
– Manoel
Jan 1 at 20:43
$begingroup$
...and Vakil's F.O.A.G.?
$endgroup$
– Armando j18eos
Jan 2 at 11:11
add a comment |
$begingroup$
In "E. Arbarello, M. Cornalba, P.A. Griffiths, J. Harris-
Geometry of Algebraic Curves Volume 1 ", page 246 is considered a morphism $f:X longrightarrow mathbb{P}^n$, where X is a quasiprojective variety. Then it is considered $Gamma$ be the closure of the graph of $f$ and denote by $widehat{Gamma}$ its normalization. Continuing, it is considered $F:widehat{Gamma} longrightarrow mathbb{P}^n$ be the induced morphism.
My questions are:
1) What is the normalization of $Gamma$?
2)What is the relationship between the two morphisms?
3)Where to read about what was done above, reference?
Thank you!
Happy New Year!
algebraic-geometry
asked Jan 1 at 20:37
ManoelManoel
922518
$endgroup$
In "E. Arbarello, M. Cornalba, P.A. Griffiths, J. Harris-
Geometry of Algebraic Curves Volume 1 ", page 246 is considered a morphism $f:X longrightarrow mathbb{P}^n$, where X is a quasiprojective variety. Then it is considered $Gamma$ be the closure of the graph of $f$ and denote by $widehat{Gamma}$ its normalization. Continuing, it is considered $F:widehat{Gamma} longrightarrow mathbb{P}^n$ be the induced morphism.
My questions are:
1) What is the normalization of $Gamma$?
2)What is the relationship between the two morphisms?
3)Where to read about what was done above, reference?
Thank you!
Happy New Year!
algebraic-geometry
algebraic-geometry
asked Jan 1 at 20:37
ManoelManoel
922518
asked Jan 1 at 20:37
ManoelManoel
922518
asked Jan 1 at 20:37
ManoelManoel
922518
asked Jan 1 at 20:37
ManoelManoel
922518
asked Jan 1 at 20:37
ManoelManoel
922518
922518
2
$begingroup$
Have you checked reference texts, Wikipedia or Stacksproject? If so, are there specific points you're confused about?
$endgroup$
– KReiser
Jan 1 at 20:40
$begingroup$
I checked Shafarevich. I could not clear the vision. The specific points are the questions I put.
$endgroup$
– Manoel
Jan 1 at 20:43
$begingroup$
...and Vakil's F.O.A.G.?
$endgroup$
– Armando j18eos
Jan 2 at 11:11
add a comment |
2
$begingroup$
Have you checked reference texts, Wikipedia or Stacksproject? If so, are there specific points you're confused about?
$endgroup$
– KReiser
Jan 1 at 20:40
$begingroup$
I checked Shafarevich. I could not clear the vision. The specific points are the questions I put.
$endgroup$
– Manoel
Jan 1 at 20:43
$begingroup$
...and Vakil's F.O.A.G.?
$endgroup$
– Armando j18eos
Jan 2 at 11:11
2
2
$begingroup$
Have you checked reference texts, Wikipedia or Stacksproject? If so, are there specific points you're confused about?
$endgroup$
– KReiser
Jan 1 at 20:40
$begingroup$
Have you checked reference texts, Wikipedia or Stacksproject? If so, are there specific points you're confused about?
$endgroup$
– KReiser
Jan 1 at 20:40
$begingroup$
I checked Shafarevich. I could not clear the vision. The specific points are the questions I put.
$endgroup$
– Manoel
Jan 1 at 20:43
$begingroup$
I checked Shafarevich. I could not clear the vision. The specific points are the questions I put.
$endgroup$
– Manoel
Jan 1 at 20:43
$begingroup$
...and Vakil's F.O.A.G.?
$endgroup$
– Armando j18eos
Jan 2 at 11:11
$begingroup$
...and Vakil's F.O.A.G.?
$endgroup$
– Armando j18eos
Jan 2 at 11:11
add a comment |
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2
$begingroup$
Have you checked reference texts, Wikipedia or Stacksproject? If so, are there specific points you're confused about?
$endgroup$
– KReiser
Jan 1 at 20:40
$begingroup$
I checked Shafarevich. I could not clear the vision. The specific points are the questions I put.
$endgroup$
– Manoel
Jan 1 at 20:43
$begingroup$
...and Vakil's F.O.A.G.?
$endgroup$
– Armando j18eos
Jan 2 at 11:11