Cohomology of Vector Bundles and Syzygies: References

By Jerzy Weyman. 2003

476 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/03bf84155daa8b4f7c0b2f243d2299fc752d0da0

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Citations in the corpus

On the ideals and singularities of secant varieties of Segre varieties (2006, methodology): “Subspace varieties are cousins of the rank varieties in [10].”
The Existence of Pure Free Resolutions (2007, methodology): “— The dual form of this result is [17], (4.”
Ranks of tensors and a generalization of secant varieties (2009, background): “We may realize σr,s(X) as the collapsing of a Grassmann bundle over σr,r(X) in the sense of [26].”
The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition (2018, background): “In this case, the ideal is rather well understood; see, e.g., [215] and also the extensive bibliography given in the book of Weyman [216].”
CM Stability and the Generalized Futaki Invariant I (2006, background): “§4 Appendix on Det and Div The references for this section are ([4], [18], [5], [7], [19], [20], and [21]).”
Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics (2008, background): “Weyman [40], especially the “basic set-up” of chapter 5 and the paper [18] of Kapranov, Sturmfels, and Zelevinsky.”
Non-commutative desingularization of determinantal varieties I (2009, methodology): “More precisely, for Mba = HomOPm−1 ( ( ∧b−1 Ω)(b), ( ∧a−1 Ω)(a) ) we compute in Theorem 3.9 the cohomology of Mba(−c) for c ∈ Z. (The interested reader may wish to compare the Appendix by Weyman to [10], which, by different methods, computes as a special case Exti( ∧p Ω, ∧q Ω) for all i > 0.)”
On the geometry of tensor network states (2011, methodology): “This type of bundle construction is standard, see [10, 16].”