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nLab > Latest Changes: symplectic singularity

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 18th 2012

    created symplectic singularity…

    … for the moment just to record references and such as to satisfy links at symplectic duality.

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeFeb 18th 2012

    Why’s it called a singularity? The word doesn’t appear in the idea section.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 18th 2012

    Unfortunately, the word also doesn’t appear in the beginning of the survey of Fu’s that I was using. I ran out of energy before being able to improve on Fu’s account…

    Hopefully Ben sees this and adds something. I shouldn’t really be spending any more time on this right now…

    • CommentRowNumber4.
    • CommentAuthorBen Webster
    • CommentTimeFeb 22nd 2012
    David-

    It's just a matter of emphasis. Singularity means the structure of an arbitrarily small neighborhood around the singular point (in commutative algebra terms, the local ring). Unlike smooth symplectic geometry, singular symplectic varieties have interesting local geometry, and it's an interesting question whether a given singularity carries a symplectic structure. Look at Definition 1.1 in the Beauville article.

1 to 4 of 4

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