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A kind of analogue of Sard's Lemma in Algebraic Geometry is Bertini's Theorem:

"Given a linear sistem |L| $|L|$ on a smooth projective variety X, its general element is smooth outside the base points".

In particular, if $|L|$ is base-point free then the set of smooth elements in $|L|$ is dense, in particular non-empty.

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A kind of analog analogue of Sard's Lemma in Algebraic Geometry is Bertini's Theorem:

"Given a linear sistem |L| on a smooth projective variety X, its general element is smooth outside the base points".

In particular, if $|L|$ is base-point free then the set of smooth elements in $|L|$ is dense, in particular non-empty.

Post Undeleted by Francesco Polizzi
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