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- W2892271030 abstract "Abstract Relative geometric invariant theory studies the behavior of semistable points under equivariant morphisms. More precisely, suppose G is a reductive linear algebraic group over an algebraically closed field k , X and Y are quasi‐projective varieties endowed with G ‐actions, is a G ‐equivariant projective morphism, the G ‐action on Y is linearized in the ample line bundle M , and the G ‐action on X is linearized in the φ‐ample line bundle L . For any positive integer n , there is an induced linearization of the G ‐action on X in the line bundle . If Y is projective and , the set of points in X that are semistable with respect to this linearization is contained in the preimage under φ of the set of points in Y that are semistable with respect to the given linearization in M . The same statement is trivially also true, if Y is affine and . In this note, we show by means of an example that the statement does not hold for arbitrary quasi‐projective varieties Y . This shows that a claim by Hu of the contrary is not true. Relative geometric invariant theory plays a role in the construction and study of degenerations of moduli spaces." @default.
- W2892271030 created "2018-09-27" @default.
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- W2892271030 date "2018-09-04" @default.
- W2892271030 modified "2023-09-25" @default.
- W2892271030 title "A remark on relative geometric invariant theory for quasi-projective varieties" @default.
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- W2892271030 doi "https://doi.org/10.1002/mana.201800054" @default.
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