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fixed grammer.
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pinaki
pinaki
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Let $f \colon X \to Y$ be a generically injective, finite morphism between projective varieties over $\mathbb{C}$, with $Y$ non-singular. Does $f$ hashave a section i.e., a morphism $g:Y \to X$ such that $f \circ g:Y \to Y$ is the identity?

If not true in general, is there any known condition under which $f$ has a section?

EDIT. The map $f$ is assumed to be dominant.

Let $f \colon X \to Y$ be a generically injective, finite morphism between projective varieties over $\mathbb{C}$, with $Y$ non-singular. Does $f$ has a section i.e., a morphism $g:Y \to X$ such that $f \circ g:Y \to Y$ is the identity?

If not true in general, is there any known condition under which $f$ has a section?

EDIT. The map $f$ is assumed to be dominant.

Let $f \colon X \to Y$ be a generically injective, finite morphism between projective varieties over $\mathbb{C}$, with $Y$ non-singular. Does $f$ have a section i.e., a morphism $g:Y \to X$ such that $f \circ g:Y \to Y$ is the identity?

If not true in general, is there any known condition under which $f$ has a section?

EDIT. The map $f$ is assumed to be dominant.

added 8 characters in body; edited title
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Francesco Polizzi
Francesco Polizzi
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Does a generically injective morphism of schemes have a section?

Let $f:X \to Y$$f \colon X \to Y$ be a generically injective, finite morphism between projective varieties over $\mathbb{C}$, with $Y$ non-singular. Does $f$ has a section i.e., a morphism $g:Y \to X$ such that $f \circ g:Y \to Y$ is the identity?

If not true in general, is there any known condition under which $f$ has a section?

EDIT. The map $f$ is assumed to be dominant.

Does a generically injective morphism of schemes have a section

Let $f:X \to Y$ be a generically injective, finite morphism between projective varieties over $\mathbb{C}$, with $Y$ non-singular. Does $f$ has a section i.e., a morphism $g:Y \to X$ such that $f \circ g:Y \to Y$ is the identity?

If not true in general, is there any known condition under which $f$ has a section?

EDIT The map $f$ is assumed to be dominant.

Does a generically injective morphism of schemes have a section?

Let $f \colon X \to Y$ be a generically injective, finite morphism between projective varieties over $\mathbb{C}$, with $Y$ non-singular. Does $f$ has a section i.e., a morphism $g:Y \to X$ such that $f \circ g:Y \to Y$ is the identity?

If not true in general, is there any known condition under which $f$ has a section?

EDIT. The map $f$ is assumed to be dominant.

added 51 characters in body
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user45397
user45397
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Let $f:X \to Y$ be a generically injective, finite morphism between projective varieties over $\mathbb{C}$, with $Y$ non-singular. Does $f$ has a section i.e., a morphism $g:Y \to X$ such that $f \circ g:Y \to Y$ is the identity?

If not true in general, is there any known condition under which $f$ has a section?

EDIT The map $f$ is assumed to be dominant.

Let $f:X \to Y$ be a generically injective, finite morphism between projective varieties over $\mathbb{C}$, with $Y$ non-singular. Does $f$ has a section i.e., a morphism $g:Y \to X$ such that $f \circ g:Y \to Y$ is the identity?

If not true in general, is there any known condition under which $f$ has a section?

Let $f:X \to Y$ be a generically injective, finite morphism between projective varieties over $\mathbb{C}$, with $Y$ non-singular. Does $f$ has a section i.e., a morphism $g:Y \to X$ such that $f \circ g:Y \to Y$ is the identity?

If not true in general, is there any known condition under which $f$ has a section?

EDIT The map $f$ is assumed to be dominant.

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user45397
user45397
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