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In the following paper: A. Mustata, M. A. Mustata, "Intermediate moduli spaces of stable maps", Invent. math. 167, 47–90 (2007) the authors introduced a variation on moduli spaces of stable maps ...

The moduli space $A_2(1,8)^{\operatorname{lev}}$ of $(1,8)$-polarized abelian surfaces with canonical level structure has a structure of conic bundle over $\mathbb{P}^2$ with a curve of degree $4$ as ...

Let us denote by $Mor_3(\mathbb{P}^1,\mathbb{P}^3)$ the spaces of degree three morphisms $f:\mathbb{P}^1\rightarrow\mathbb{P}^3$, $$f(x_0,x_1)=[f_0(x_0,x_1):f_1(x_0,x_1):f_2(x_0,x_1):f_3(x_0,x_1)]$$ ...