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The formulas we obtained are conjectured by m This already shows that for $g \geq 5$, not every genus $g$ curve is hyperelliptic. In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves

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It is thus a special case of a moduli space. We achieve this result by computing the cohomological invariants of this stack. In the course, we de ne the moduli space and discuss its basic properties

We present many of the basic constructions related to it, e.g

Of gluing and forgetful maps, and explain a number of examples of these moduli spaces in more details. These notes describe the classical approach to moduli for curves of genus 2 and 3, following the papers [igu60] en [gk06] In the final section, an interesting link to del pezzo surfaces is described. We treat some general facts about moduli spaces, in particular moduli of curves of genus g

We give some examples, and construct coarse moduli spaces for curves of genus zero and elliptic curves We introduce briefly the concept of algebraic stack. In particular, given a family of curves f