Remarks on Type III Unprojection

Details Remarks on Type III Unprojection Remarks on Type III Unprojection

2005-01-29

arxiv.org/abs/math/0501535v1

Mathematics

Algebraic Geometry

11 pages, to appear in Communications in Algebra

Scientific paper

Type III unprojection plays a very important role in the birational geometry of Fano threefolds. It was first introduced by A. Corti on his calculations of Fano threefolds of genus 6 and 7. It seems that at present a general definition of the type III unprojection is still missing. After proving some general facts about residual ideals, we propose a definition for the generic Type III unprojection, and prove that it gives a Gorenstein ring.

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