On intrinsic quadrics

Abstract

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.

31 pages, references added

References in corpus (2)

• Smooth projective varieties with a torus action of complexity 1 and Picard number 2
• On Fujita's freeness conjecture in dimension 5

Cited by in corpus (2)

• On torus actions of higher complexity
• On smooth Fano fourfolds of Picard number two