
TL;DR
This paper constructs and analyzes moduli spaces of projective varieties with finite group actions, introducing G-marked models, proving their existence, and exploring their structure and decomposition.
Contribution
It introduces the moduli functor for G-marked models, proves the existence of the coarse moduli scheme, and studies its structure via a canonical decomposition.
Findings
Existence of the coarse moduli scheme $rak{M}_h[G]$ for G-marked models.
Proper and finite morphism from $rak{M}_h[G]$ to $rak{M}_h$ with a closed image.
Canonical decomposition $rak{D}_h[G]$ of the moduli space.
Abstract
The aim of this paper is to investigate the closed subschemes of moduli spaces corresponding to projective varieties which admit an effective action by a given finite group . To achieve this, we introduce the moduli functor of -marked Gorenstein canonical models with Hilbert polynomial , and prove the existence of , the coarse moduli scheme for . Then we show that has a proper and finite morphism onto so that its image is a closed subscheme. In the end we obtain the canonical representation type decomposition of and use to study the structure of .
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