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• W2967332022 abstract "The aim of this thesis is to explore the moduli of pointed real curves of genus zero. We investigate the actions of a set of natural real structures cσ : (Σ; ps1 , · · · , psn) 7→ (Σ; pσ(s1), · · · , pσ(sn)), on the moduli space MS of stable S-pointed complex curves of genus zero where σ is an involution acting on the labeling set S = {s1, · · · , sn}. First, we determine the moduli functor of σ-equivariant families represented by the real variety (MS, cσ). We introduce the fixed point set RM σ S of the real structure cσ as the moduli space of σ-invariant real curves. We introduce a natural combinatorial stratification of the real moduli space RMσS through the stratification of MS. Each stratum gives the equisingular deformations of σ-invariant real curves. We identify the strata of RMσS with the products of spaces of Z2-equivariant point configurations in the projective line CP and the moduli spaces MS′ . The degeneration types of σ-invariant real curves are encoded by trees with corresponding decorations. We calculate the first Stiefel-Whitney class of RMσS in terms of its strata. We construct the orientation double cover RM S of RM σ S, and show that the moduli space RMσS is not orientable for |S| ≥ 5 and Fix(σ) 6= ∅. The double covering which is constructed in this work significantly differs from the ‘double covering’ in the recent literature on open Gromov-Witten invariants and moduli spaces of pseudoholomorphic discs: Our double covering has no boundary which is better suited for the application of intersection theory. We then explore the further topological properties of RMσS. We construct a graph complex G• generated by the fundamental classes of the strata of RM σ S. We show that the homology of RMσS is isomorphic to the homology of the graph complex G•. Finally, we give presentations of the fundamental groups of the real moduli space RMσS and its orientation double cover RM S ." @default.
• W2967332022 created "2019-08-22" @default.
• W2967332022 creator A5051441731 @default.
• W2967332022 date "2006-01-01" @default.
• W2967332022 modified "2023-09-23" @default.
• W2967332022 title "On moduli of pointed real curves of genus zero" @default.
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• W2967332022 hasPublicationYear "2006" @default.
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