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On Moduli Spaces of Weighted Pointed Stable Curves and Applications
He, Zhuang

2015, Master of Science, Ohio State University, Mathematics.
Moduli spaces of curves have been central objects for decades in algebraic geometry.

This paper reviews a generalization by Hassett in 2003 of the classic moduli problem. Hassett's moduli spaces classify the stable n-pointed curves of given genus g, with weighted data on the marked points. Hassett proved the existence of such coarse moduli spaces as projective schemes.

In the first chapters we review the classic moduli problems and provide a sketch of GIT construction of moduli spaces. Then we review the reductions maps between moduli space of weighted pointed stable curves. Next we discuss the chamber decomposition and wall crossing maps among our moduli spaces.

The last sections provided an exposition of the application to several birational constructions of moduli spaces. We review Kapranov, Keel, and Losev-Manin's examples, and discuss the realizations of their examples by successive reductions between weighted pointed moduli spaces.
Hsian-Hua Tseng (Advisor)
Jean-Fran├žois Lafont (Committee Member)
57 p.

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He, Z. (2015). On Moduli Spaces of Weighted Pointed Stable Curves and Applications. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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He, Zhuang. "On Moduli Spaces of Weighted Pointed Stable Curves and Applications." Electronic Thesis or Dissertation. Ohio State University, 2015. OhioLINK Electronic Theses and Dissertations Center. 21 Sep 2017.

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He, Zhuang "On Moduli Spaces of Weighted Pointed Stable Curves and Applications." Electronic Thesis or Dissertation. Ohio State University, 2015. https://etd.ohiolink.edu/

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