On the moduli of hypersurfaces in toric orbifolds
We construct and study the moduli of stable hypersurfaces in toric orbifolds. Let X be a projective toric orbifold and $\alpha \in \operatorname{Cl}(X)$ an ample class. The moduli space is constructed as a quotient of the linear system $|\alpha|$ by $G = \operatorname{Aut}(X)$. Since the group G is...
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| Vydáno v: | Proceedings of the Edinburgh Mathematical Society Ročník 67; číslo 2; s. 577 - 616 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cambridge, UK
Cambridge University Press
01.05.2024
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| Témata: | |
| ISSN: | 0013-0915, 1464-3839 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | We construct and study the moduli of stable hypersurfaces in toric orbifolds. Let X be a projective toric orbifold and $\alpha \in \operatorname{Cl}(X)$ an ample class. The moduli space is constructed as a quotient of the linear system $|\alpha|$ by $G = \operatorname{Aut}(X)$. Since the group G is non-reductive in general, we use new techniques of non-reductive geometric invariant theory. Using the A-discriminant of Gelfand, Kapranov and Zelevinsky, we prove semistability for quasismooth hypersurfaces of toric orbifolds. Further, we prove the existence of a quasi-projective moduli space of quasismooth hypersurfaces in a weighted projective space 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. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0013-0915 1464-3839 |
| DOI: | 10.1017/S0013091524000166 |