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Weierstrass cycles and tautological rings in various moduli spaces of algebraic curves

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We analyze Weierstrass cycles and tautological rings in moduli spaces of smooth algebraic curves and in moduli spaces of integral algebraic curves with embedded disks with special attention to moduli spaces of curves having genus less than or equal to 6. In particular, we show that our general formula gives a good estimate for the dimension of Weierstrass cycles for low genera.

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