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- W2078760108 abstract "We discuss the stabilization of symmetric products Sym^n(X) of a smooth projective variety X in the Grothendieck ring of varieties. For smooth projective surfaces X with non-zero h^0(X, omega_X), these products do not stabilize; we conditionally show that they do not stabilize in another related sense, in response to a question of R. Vakil and M. Wood. There are analogies between such stabilization, the Dold-Thom theorem, and the analytic class number formula. Finally, we discuss Hodge-theoretic obstructions to the stabilization of symmetric products, and provide evidence for these obstructions in terms of a relationship between the Newton polygon of a certain motivic zeta function associated to a curve, and its Hodge polygon." @default.
- W2078760108 created "2016-06-24" @default.
- W2078760108 creator A5013284360 @default.
- W2078760108 date "2012-09-21" @default.
- W2078760108 modified "2023-09-27" @default.
- W2078760108 title "Symmetric Powers Do Not Stabilize" @default.
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