ScalingStacks

Definition 2.1 . [0599]

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Definition 2.1.

Let YY be a reduced scheme of locally finite type over a field κ\kappa. Set Y(0):=YY^{(0)}:=Y and let Y(i+1)Y^{(i+1)} be the complement of the set of normal points in Y(i)Y^{(i)}. The irreducible components of Y(i)∖Y(i+1)Y^{(i)}\setminus Y^{(i+1)} are called strata of YY. There is a partial ordering on the set of strata given by R1≤R2R_{1}\leq R_{2} if and only if R1¯⊆R2¯\overline{R_{1}}\subseteq\overline{R_{2}}. A cycle Z∈Z⁡(Y)Z\in Z(Y) is called a strata cycle if there are strata S1,…,SnS_{1},...,S_{n} of YY such that Z=∑mi​Si¯Z=\sum m_{i}\overline{S_{i}} with mi∈ℝm_{i}\in\mathbb{R}.

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