Is the morphism $X_1amalg X_2to Y_1amalg Y_2$ induced by $f_1$ and $f_2$ projective?
$begingroup$
Let $f_1:X_1to Y_1$ and $f_2: X_2to Y_2$ are projective morphisms of schemes. Here a projective morphism $f: Xto Y$ means $f$ can be factorized as $X to mathrm{P}_Y^nto Y$ for some closed immersion $Xto mathrm{P}_Y^n$.
Let $X_1amalg X_2$ denotes the disjoint union of $X_1$ and $X_2$, and $Y_1amalg Y_2$ denote the disjoint union of $Y_1$ and $Y_2$.
Is the morphism $X_1amalg X_2to Y_1amalg Y_2$ induced by $f_1$ and $f_2$ projective?
algebraic-geometry
asked Jan 23 at 16:59
Born to be proudBorn to be proud
854510
$endgroup$
add a comment |
$begingroup$
Let $f_1:X_1to Y_1$ and $f_2: X_2to Y_2$ are projective morphisms of schemes. Here a projective morphism $f: Xto Y$ means $f$ can be factorized as $X to mathrm{P}_Y^nto Y$ for some closed immersion $Xto mathrm{P}_Y^n$.
Let $X_1amalg X_2$ denotes the disjoint union of $X_1$ and $X_2$, and $Y_1amalg Y_2$ denote the disjoint union of $Y_1$ and $Y_2$.
Is the morphism $X_1amalg X_2to Y_1amalg Y_2$ induced by $f_1$ and $f_2$ projective?
algebraic-geometry
asked Jan 23 at 16:59
Born to be proudBorn to be proud
854510
$endgroup$
1
$begingroup$
What have you tried? Do you see any way to construct a map from the union of the $X_i$ into a $Bbb P^N_{coprod Y_i}$ for some $N$?
$endgroup$
– KReiser
Jan 23 at 21:13
add a comment |
$begingroup$
Let $f_1:X_1to Y_1$ and $f_2: X_2to Y_2$ are projective morphisms of schemes. Here a projective morphism $f: Xto Y$ means $f$ can be factorized as $X to mathrm{P}_Y^nto Y$ for some closed immersion $Xto mathrm{P}_Y^n$.
Let $X_1amalg X_2$ denotes the disjoint union of $X_1$ and $X_2$, and $Y_1amalg Y_2$ denote the disjoint union of $Y_1$ and $Y_2$.
Is the morphism $X_1amalg X_2to Y_1amalg Y_2$ induced by $f_1$ and $f_2$ projective?
algebraic-geometry
asked Jan 23 at 16:59
Born to be proudBorn to be proud
854510
$endgroup$
Let $f_1:X_1to Y_1$ and $f_2: X_2to Y_2$ are projective morphisms of schemes. Here a projective morphism $f: Xto Y$ means $f$ can be factorized as $X to mathrm{P}_Y^nto Y$ for some closed immersion $Xto mathrm{P}_Y^n$.
Let $X_1amalg X_2$ denotes the disjoint union of $X_1$ and $X_2$, and $Y_1amalg Y_2$ denote the disjoint union of $Y_1$ and $Y_2$.
Is the morphism $X_1amalg X_2to Y_1amalg Y_2$ induced by $f_1$ and $f_2$ projective?
algebraic-geometry
algebraic-geometry
asked Jan 23 at 16:59
Born to be proudBorn to be proud
854510
asked Jan 23 at 16:59
Born to be proudBorn to be proud
854510
edited Jan 23 at 17:26
Born to be proud
asked Jan 23 at 16:59
Born to be proudBorn to be proud
854510
asked Jan 23 at 16:59
Born to be proudBorn to be proud
854510
asked Jan 23 at 16:59
Born to be proudBorn to be proud
854510
854510
1
$begingroup$
What have you tried? Do you see any way to construct a map from the union of the $X_i$ into a $Bbb P^N_{coprod Y_i}$ for some $N$?
$endgroup$
– KReiser
Jan 23 at 21:13
add a comment |
1
$begingroup$
What have you tried? Do you see any way to construct a map from the union of the $X_i$ into a $Bbb P^N_{coprod Y_i}$ for some $N$?
$endgroup$
– KReiser
Jan 23 at 21:13
1
1
$begingroup$
What have you tried? Do you see any way to construct a map from the union of the $X_i$ into a $Bbb P^N_{coprod Y_i}$ for some $N$?
$endgroup$
– KReiser
Jan 23 at 21:13
$begingroup$
What have you tried? Do you see any way to construct a map from the union of the $X_i$ into a $Bbb P^N_{coprod Y_i}$ for some $N$?
$endgroup$
– KReiser
Jan 23 at 21:13
add a comment |
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$begingroup$
What have you tried? Do you see any way to construct a map from the union of the $X_i$ into a $Bbb P^N_{coprod Y_i}$ for some $N$?
$endgroup$
– KReiser
Jan 23 at 21:13