Abstract
The study of the moduli space plays an important role in classical enumerative geometry and its interaction with string theory in physics. Given X = [ℙ1/ℤr] and let x′ = ([0]a, [∞]b) the 2-tuple of twisted sectors on X, we construct in this paper two different compactifications of the moduli space M0,2(X, d[ℙ1/ℤr], x′): Nonlinear Sigma Model Mdx′ and Linear Sigma Model Ndx′. Relations between Mdx′ and Ndx′ are studied and a new gluing recursive relation on Ndx′ is derived from Mdx′ due to virtual localization formula.
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