Local property of a flat family of schemes
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$begingroup$
Let $pi: X to S$ be a flat, smooth family of genus $0$ curves, for example. Now take a point $x in S$, then $x in pi{-1}(p)$ from some $p in S$, i.e $x in mathbb{P}^1$.
I am trying to relate such families to first order infinitesimal deformations.
In particular, does there exist an open subset $ xin U subset X$ such that $U$ is a first order infinitesimal deformation of $mathbb{P}^1$?
algebraic-geometry commutative-algebra deformation-theory
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,01611024
$endgroup$
add a comment |
$begingroup$
Let $pi: X to S$ be a flat, smooth family of genus $0$ curves, for example. Now take a point $x in S$, then $x in pi{-1}(p)$ from some $p in S$, i.e $x in mathbb{P}^1$.
I am trying to relate such families to first order infinitesimal deformations.
In particular, does there exist an open subset $ xin U subset X$ such that $U$ is a first order infinitesimal deformation of $mathbb{P}^1$?
algebraic-geometry commutative-algebra deformation-theory
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,01611024
$endgroup$
$begingroup$
In your first paragraph, $x in S$ and (presumably) $x in pi^{-1}(p)$, which doesn't make sense.
$endgroup$
– RghtHndSd
Dec 12 '18 at 3:31
add a comment |
$begingroup$
Let $pi: X to S$ be a flat, smooth family of genus $0$ curves, for example. Now take a point $x in S$, then $x in pi{-1}(p)$ from some $p in S$, i.e $x in mathbb{P}^1$.
I am trying to relate such families to first order infinitesimal deformations.
In particular, does there exist an open subset $ xin U subset X$ such that $U$ is a first order infinitesimal deformation of $mathbb{P}^1$?
algebraic-geometry commutative-algebra deformation-theory
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,01611024
$endgroup$
Let $pi: X to S$ be a flat, smooth family of genus $0$ curves, for example. Now take a point $x in S$, then $x in pi{-1}(p)$ from some $p in S$, i.e $x in mathbb{P}^1$.
I am trying to relate such families to first order infinitesimal deformations.
In particular, does there exist an open subset $ xin U subset X$ such that $U$ is a first order infinitesimal deformation of $mathbb{P}^1$?
algebraic-geometry commutative-algebra deformation-theory
algebraic-geometry commutative-algebra deformation-theory
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,01611024
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,01611024
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,01611024
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,01611024
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,01611024
2,01611024
$begingroup$
In your first paragraph, $x in S$ and (presumably) $x in pi^{-1}(p)$, which doesn't make sense.
$endgroup$
– RghtHndSd
Dec 12 '18 at 3:31
add a comment |
$begingroup$
In your first paragraph, $x in S$ and (presumably) $x in pi^{-1}(p)$, which doesn't make sense.
$endgroup$
– RghtHndSd
Dec 12 '18 at 3:31
$begingroup$
In your first paragraph, $x in S$ and (presumably) $x in pi^{-1}(p)$, which doesn't make sense.
$endgroup$
– RghtHndSd
Dec 12 '18 at 3:31
$begingroup$
In your first paragraph, $x in S$ and (presumably) $x in pi^{-1}(p)$, which doesn't make sense.
$endgroup$
– RghtHndSd
Dec 12 '18 at 3:31
add a comment |
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$begingroup$
In your first paragraph, $x in S$ and (presumably) $x in pi^{-1}(p)$, which doesn't make sense.
$endgroup$
– RghtHndSd
Dec 12 '18 at 3:31