• DOI:10.17169/REFUBIUM-27089
• Corpus ID: 173991080

Moduli of hypersurfaces in toric orbifolds

@article{Bunnett2019ModuliOH,
  title={Moduli of hypersurfaces in toric orbifolds},
  author={Dominic Bunnett},
  journal={arXiv: Algebraic Geometry},
  year={2019}
}

• Dominic Bunnett
• Published 1 June 2019
• Mathematics
• arXiv: Algebraic Geometry

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 weighted projective space are stable when the weighted projective space satisfies a certain condition. We also discuss how to proceed when this condition is not satisfied. We prove that the automorphism group of a quasismooth hypersurface of weighted projective space is finite excluding some low degrees.