Abstract
After introducing an equivalence problem for symplectic singularities, we formulate an algebraic version of such a problem. Let be an affine normal variety with a -action having only positive weights. Assume that the regular part of admits an algebraic symplectic -form with weight . Our main theorem asserts that any algebraic symplectic -form on of weight is equivalent to up to a -equivariant automorphism of if . When we have a counterexample to this statement. In the latter half of the article, we discuss the equivalence problem up to constant. We associate to a projective variety and prove that has a contact orbifold structure. Moreover, when has canonical singularities, the contact orbifold structure is rigid under a small deformation. The equivalence problem is then reduced to the uniqueness of the contact structures. In most examples the symplectic structures turn out to be unique up to constant with very few exceptions. In the final section we pose a splitting conjecture for symplectic singularities.
Citation
Yoshinori Namikawa. "Equivalence of symplectic singularities." Kyoto J. Math. 53 (2) 483 - 514, Summer 2013. https://doi.org/10.1215/21562261-2081270
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