---
date: 2022-05-25 20:09
modification date: Wednesday 25th May 2022 20:09:12
title: "stable del Pezzo pair"
aliases: [stable del Pezzo pair]
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- Refs:
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# stable del Pezzo pair

Fixing a degree $e \in \ZZ_{\geq 0}$ and a rational $\eps \in (0, 1] \intersect \QQ$, a **stable del Pezzo pair of type $(e, \eps)$** is a pair $\qty{Y, C + \qty{1+\eps\over 2}B}$ such that

- $2(K_X + C) + B \sim 0$
- $B$ is an [ample](Unsorted/ample.md) [Cartier divisor](Unsorted/Weil%20divisor.md) of degree $B^2 = e$.
- This forms a [stable pair](Unsorted/stable%20pair.md).