منابع مشابه
Kustin–Miller unprojection with complexes
A main ingredient for Kustin–Miller unprojection, as developed in [PR], is the module HomR(I, ωR), where R is a local Gorenstein ring and I a codimension one ideal with R/I Gorenstein. We prove a method of calculating it in a relative setting using resolutions. We give three applications. In the first we generalise a result of [CFHR]. The second and the third are about Tom and Jerry, two famili...
متن کاملKustin–Miller unprojection without complexes
Gorenstein projection plays a key role in birational geometry; the typical example is the linear projection of a del Pezzo surface of degree d to one of degree d− 1, but variations on the same idea provide many of the classical and modern birational links between Fano 3-folds. The inverse operation is the Kustin–Miller unprojection theorem, which constructs “more complicated” Gorenstein rings s...
متن کاملParallel Kustin–miller Unprojection with an Application to Calabi–yau Geometry
Kustin–Miller unprojection constructs more complicated Gorenstein rings from simpler ones. Geometrically, it inverts certain projections, and appears in the constructions of explicit birational geometry. However, it is often desirable to perform not only one but a series of unprojections. The main aim of the present paper is to develop a theory, which we call parallel Kustin–Miller unprojection...
متن کاملStellar subdivisions and Stanley-Reisner rings of Gorenstein complexes
Unprojection theory analyzes and constructs complicated commutative rings in terms of simpler ones. Our main result is that, on the algebraic level of Stanley-Reisner rings, stellar subdivisions of Gorenstein* simplicial complexes correspond to unprojections of type Kustin-Miller. As an application of our methods we study the minimal resolution of Stanley– Reisner rings associated to stacked po...
متن کاملBirational Modifications of Surfaces via Unprojections
We describe elementary transformations between minimal models of rational surfaces in terms of unprojections. These do not fit into the framework of Kustin–Miller unprojections as introduced by Papadakis and Reid, since we have to leave the world of projectively Gorenstein varieties. Also, our unprojections do not depend on the choice of the unprojection locus only, but need extra data correspo...
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ژورنال
عنوان ژورنال: Journal of Algebraic Geometry
سال: 2004
ISSN: 1056-3911,1534-7486
DOI: 10.1090/s1056-3911-03-00350-3