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Moduli of elliptic curves in products of projective spaces

Moduli of elliptic curves in products of projective spaces

We exhibit a smooth compactification of the moduli space of elliptic curves in a product of projective spaces with tangency along a subset of its toric boundary divisors. This is a Vakil--Zinger type of desingularization for maps to a product of projective spaces using ideas of elliptic singularities and logarithmic …