Intersection-theoretical computations on \Mgbar

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We determine necessary conditions for ample divisors in arbitrary genus as well as for very ample divisors in genus 2 and 3. We also compute the intersection numbers $λ^9$ and $λ_{g-1}^3$ in genus 4. The latter number is relevant for counting curves of higher genus on manifolds, cf. the recent work of Bershadsky et al.
13 pages, no figures. To appear in "Parameter Spaces", Banach Center Publications, volume in preparation. plain tex

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