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Computing invariants via slicing groupoids: Gel'fand MacPherson, Gale and positive characteristic stable maps
Author(s) -
Alper Jarod
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201000058
Subject(s) - mathematics , moduli space , cover (algebra) , affine transformation , space (punctuation) , combinatorics , moduli , affine space , embedding , algebra over a field , pure mathematics , physics , computer science , quantum mechanics , mechanical engineering , engineering , operating system , artificial intelligence
We offer a groupoid‐theoretic approach to computing invariants. We illustrate this approach by describing the Gel'fand‐MacPherson correspondence and the Gale transform. We also provide Zariski‐local descriptions of the moduli space of ordered points in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {P}^1$\end{document} . We give an explicit description of the moduli space \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$M_0(\mathbb {P}^1,2)$\end{document} over \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mbox{Spec}\mathbb {Z}$\end{document} . In characteristic 2, the singularity at the totally ramified cover is isomorphic to the affine cone over the Veronese embedding \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {P}^1 \rightarrow \mathbb {P}^4$\end{document} .