8 papers · 1 filter
Weighted Grassmannians
Alessio Corti, Miles Reid
Many classes of projective algebraic varieties can be studied in terms of graded rings. Gorenstein graded rings in small codimension have been studied recently from an algebraic po…
Update on 3-folds
Miles Reid
The division of compact Riemann surfaces into 3 cases K_C<0, g=0, or K_C=0, g=1, or K_C>0, g>=2 is well known, and corresponds to the familiar trichotomy of spherical, Euclidean an…
Fano 3-folds, K3 surfaces and graded rings
Selma Altınok, Gavin Brown, Miles Reid
Explicit birational geometry of 3-folds represents a second phase of Mori theory, going beyond the foundational work of the 1980s. This paper is a tutorial and colloquial introduct…
Kustin-Miller unprojection with complexes
Stavros Papadakis
A main ingredient for Kustin-Miller unprojection, as developed in (S. Papadakis and M. Reid, Kustin-Miller unprojection without complexes, math.AG/0011094), is the module Hom_R(I,…
Kustin--Miller unprojection without complexes
Stavros Papadakis, Miles Reid
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…
How to calculate A-Hilb C^3
Alastair Craw, Miles Reid
Iku Nakamura [Hilbert schemes of Abelian group orbits, J. Alg. Geom. 10 (2001), 757--779] introduced the G-Hilbert scheme for a finite subgroup G in SL(3,C), and conjectured that i…