Equivalent Birational Embeddings III: cones

Abstract

Two divisors in ${\mathbb{P}}^n$ are said to be Cremona equivalent if there is a Cremona modification sending one to the other. In this paper I study irreducible cones in ${\mathbb{P}}^n$ and prove that two cones are Cremona equivalent if their general hyperplane sections are birational. In particular I produce examples of cones in ${\mathbb{P}}^3$ Cremona equivalent to a plane whose plane section is not Cremona equivalent to a line in ${\mathbb{P}}^2$.

References in corpus (2)

• Existence of minimal models for varieties of log general type
• On rational cuspidal curves, open surfaces and local singularities