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Regular version of the site

Book chapter

Contracting the Weierstrass locus to a point

P. 241-257.
Polishchuk A.

We construct an open substack $U\subset\mathcal{M}_{g,1}$ with the complement of codimension $\ge 2$ and a morphism from $U$ to a weighted projective stack, which sends the Weierstrass locus $\mathcal{W}\cap U$ to a point, and maps $\mathcal{M}_{g,1}\setminus\mathcal{W}$ isomorphically to its image. The proof uses alternative birational models of $\mathcal{M}_{g,1}$ and $\mathcal{M}_{g,2}$ from arXiv:1509.07241.

In book

Edited by: A. Kashani-Poor, R. Minasian, N. Nekrasov et al. American Mathematical Society, 2018.