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stable del Pezzo pair

Fixing a degree \(e \in {\mathbf{Z}}_{\geq 0}\) and a rational \({\varepsilon}\in (0, 1] \cap{\mathbf{Q}}\), a stable del Pezzo pair of type \((e, {\varepsilon})\) is a pair \(\qty{Y, C + \qty{1+{\varepsilon}\over 2}B}\) such that

• \(2(K_X + C) + B \sim 0\)
• \(B\) is an ample Cartier divisor of degree \(B^2 = e\).
• This forms a stable pair.