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In general, how to prove a variety has rational singularities intrinsically? i.e., don't use the Artin's criterion concerning the exceptional locus. And what kinds of varieties have only rational singularities? I've read a proof of classification of normal cubic surfaces (paper of Bruce and Wall), but their method is quite concrete, is there any way to prove the fact that a normal cubic surface which is not a cone can only contain rational singularities without using the classification of du Val singularities?

In general, how to prove a variety has rational singularities intrinsically? i.e., don't use the Artin's criterion concerning the exceptional locus. And what kinds of varieties have only rational singularities? I've read a proof of classification of normal cubic surfaces (paper of Bruce and Wall), but their method is quite concrete, is there any way to prove the fact that a cubic surface can only contain rational singularities without using the classification of du Val singularities?

In general, how to prove a variety has rational singularities intrinsically? i.e., don't use the Artin's criterion concerning the exceptional locus. And what kinds of varieties have only rational singularities? I've read a proof of classification of normal cubic surfaces (paper of Bruce and Wall), but their method is quite concrete, is there any way to prove the fact that a normal cubic surface which is not a cone can only contain rational singularities without using the classification of du Val singularities?

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user50489
user50489
  • 11
  • 2

Intrinsically proving a singularity is rational

In general, how to prove a variety has rational singularities intrinsically? i.e., don't use the Artin's criterion concerning the exceptional locus. And what kinds of varieties have only rational singularities? I've read a proof of classification of normal cubic surfaces (paper of Bruce and Wall), but their method is quite concrete, is there any way to prove the fact that a cubic surface can only contain rational singularities without using the classification of du Val singularities?