We generalize the classical semicontinuity theorem for GIT (semi)stable loci under variations of linearizations to a relative situation of an equivariant projective morphism over an affine base. As an application to moduli problems, we consider degenerations of Hilbert schemes and give a conceptual interpretation of the (semi)stable loci of the degeneration families constructed in [GHH19].
Halle, L., Hulek, K., Zhang Ziyu (2023). Relative VGIT and an Application to Degenerations of Hilbert Schemes. MICHIGAN MATHEMATICAL JOURNAL, 73(1), 67-97 [10.1307/mmj/20205898].
Relative VGIT and an Application to Degenerations of Hilbert Schemes
Halle, Lars
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2023
Abstract
We generalize the classical semicontinuity theorem for GIT (semi)stable loci under variations of linearizations to a relative situation of an equivariant projective morphism over an affine base. As an application to moduli problems, we consider degenerations of Hilbert schemes and give a conceptual interpretation of the (semi)stable loci of the degeneration families constructed in [GHH19].File in questo prodotto:
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