Intersection Theory of Moduli Space of Stable N-Pointed Curves of Genus Zero

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Hassani, Mahyar | 2020

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 52890 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Jafari, Amir
Abstract:
A moduli spase consists in classifying geometric objects up tp equivalence relations and its point are in 1-1 corrospondence with equivalence classes. One of the most important moduli spaces in algebraic geometry is «moduli space of stable n-pointed curves of genus zero» which has many applications in mathematics and theoretical physics.In [10] Knudsen shows that for every n 3 there is a smooth projective variety Xn that is a moduli space for stable n-pointed curves of genus zero.In this thesis we study moduli spaces and introduce Xn and its relation with cross ratios. This way we show Xn is smooth projective variety and a fine moduli space. [5] After that we study a paper by Sean Keel. [9] We introduce his alternative construction of Xn via a sequence of smooth blow-ups and we explain why cycle map from chow groups to homology A(Xn) ! H(Xn) is an isomorphism. At the end we compute chow ring of Xn by this description of blow-up
Keywords:
Variety ; Blow Up (Mathematics) ; Moduli Space ; Curvature ; Chow Group ; Cross Ratio ; Intersection Theory