On the moduli of hypersurfaces in toric orbifolds
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866909207320592384 |
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| author | Bunnett, Dominic |
| author_facet | Bunnett, Dominic |
| contents | We construct and study the moduli of hypersurfaces in toric orbifolds. Let $X$ be a projective toric orbifold and $α\in Cl(X)$ an ample class. The moduli space is constructed as a quotient of the linear system $|α|$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_00272 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On the moduli of hypersurfaces in toric orbifolds Bunnett, Dominic Algebraic Geometry We construct and study the moduli of hypersurfaces in toric orbifolds. Let $X$ be a projective toric orbifold and $α\in Cl(X)$ an ample class. The moduli space is constructed as a quotient of the linear system $|α|$ 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. |
| title | On the moduli of hypersurfaces in toric orbifolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1906.00272 |