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Working paper

Birational models of M_2,2 arising as moduli of curves with nonspecial divisors

Polishchuk A., Johnson D.
We study birational projective models of M_2,2 obtained from the moduli space of curves with nonspecial divisors. We describe geometrically which singular curves appear in these models and show that one of them is obtained by blowing down the Weierstrass divisor in the moduli stack of Z-stable curves \bar{M}_2,2(Z) defined by Smyth. As a corollary, we prove projectivity of the coarse moduli space \bar{M}_2,2(Z).