An intrinsic quadric is a normal projective variety with a Cox ring defined by a single quadratic relation. We provide explicit descriptions of these varieties in the smooth case for small Picard numbers. As applications, we figure out in this setting the Fano examples and (affirmatively) test Fujita's base point free conjecture.

中文翻译：

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关于内在二次曲线

内在二次曲线是具有由单个二次关系定义的 Cox 环的正规射影变体。我们在小皮卡德数的平滑情况下提供了这些变体的明确描述。作为应用程序，我们在此设置中找出 Fano 示例并（肯定地）测试 Fujita 的无基点猜想。