Real Quotient Singularities and Nonsingular Real Algebraic Curves in the Boundary of the Moduli Space
Tóm tắt
The quotient of a real analytic manifold by a properly discontinuous group action is, in general, only a semianalytic variety. We study the boundary of such a quotient, i.e., the set of points at which the quotient is not analytic. We apply the results to the moduli space Mg/∝ of nonsingular real algebraic curves of genus g (g≤2). This moduli space has a natural structure of a semianalytic variety. We determine the dimension of the boundary of any connected component of Mg/∝. It turns out that every connected component has a nonempty boundary. In particular, no connected component of Mg/∝ is real analytic. We conclude that Mg/∝ is not a real analytic variety.
Tài liệu tham khảo
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