# Moduli of hypersurfaces in toric orbifolds

@article{Bunnett2019ModuliOH,
title={Moduli of hypersurfaces in toric orbifolds},
author={Dominic Bunnett},
journal={arXiv: Algebraic Geometry},
year={2019}
}
We construct and study the moduli of hypersurfaces in toric orbifolds. Let $X$ be a projective toric orbifold and $\alpha \in Cl(X)$ an ample class. The moduli space is constructed as a quotient of the linear system $|\alpha|$ by $G = Aut(X)$. Since the group $G$ is non-reductive in general, we use new techniques of non-reductive geometric invariant theory. Using the $A$-discriminant we prove semistability for certain toric orbifolds. Further, we show that quasismooth hypersurfaces in a…

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