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This tag is used if a reference is needed in a paper or textbook on a specific result.

9 votes

Matrix factorizations and physics

Here's a video of a talk by Kentaro Hori at MSRI: Matrix Factorizations and Complexes of Vector Bundle ---- An Approach from 2d QFT with Boundary. It's not strictly what you're asking for, but does s …
Graham Leuschke's user avatar
9 votes

Free Resolution of this determinantal variety.

Macaulay2, version 1.3.1 with packages: ConwayPolynomials, Elimination, IntegralClosure, LLLBases, PrimaryDecomposition, ReesAlgebra, SchurRings, TangentCone i1 : S = QQ[x_(1,1)..x_(3 …
Graham Leuschke's user avatar
7 votes

The finite subgroups of SL(2,C)

The McKay correspondence mentioned in Hailong's and Mike's answers extends to maximal Cohen-Macaulay modules over the invariant rings $R=k[x,y]^G$, where $G$ is a finite subgroup of $GL(2,k)$ (with $| …
Graham Leuschke's user avatar
4 votes

Krull-Schmidt Analogue for Complete / Graded Rings

Self-advertisement alert: In Chapter 1 of my book with Roger Wiegand we give a complete proof for complete local rings. It follows from a more general fact about additive categories in which every id …
Graham Leuschke's user avatar
2 votes
Accepted

Is there a nice way to characterise the derived equivalence induced by a flop?

As always, it depends on what you think "explicitly" means. It's a Fourier-Mukai transform; see, for example, Van den Bergh and Hille's expository article. It can also be explained in terms of so-cal …
Graham Leuschke's user avatar
2 votes

The Jacobian ideal generates the socle of a complete intersection

I'm promoting this comment to an answer, since it appears no one else is jumping in with a proof. Prop. 2 of this paper by Eisenbud attributes it 'essentially' to Berger, and has a sketch of a proof. …
Graham Leuschke's user avatar