In this chapter we introduce the main tool of Geometric Invariant Theory (the Fundamental Formula, see Theorem 1.6) that we shall apply in Chapter 2 to a specific "moduli problem" in order to get the Roth's Theorem: it is a formula relating the height of a semistable point with the height of its projection on the GIT quotient. In this general framework we also state and prove a lower bound of the height on the quotient (see Theorem 2.1).
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