Essentialism(e)? Editorial

Knutson, Susan; Mezei, Kathy; Godard, Barbara

doi:10.25071/1923-9408.23647

Cited by 1 publication

(4 citation statements)

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“…Finally, as this paper was being finished, a paper appeared [102] which claims to give an intuitive understanding of ordinary mirror symmetry as a particular form of T-duality. It may be possible to apply their ideas to our technology to gain insight into (0,2) mirror symmetry; work on this is in progress [16]. algebraic groups are reductive: a basic example is C under +.…”

Section: Discussionmentioning

confidence: 99%

“…How can this map be seen in the present language? First, note that the sheaf compatibility conditions in equation (16)…”

Section: Torsion-free Sheaves On Smooth Toric Varietiesmentioning

confidence: 99%

“…To describe moduli spaces of equivariant torsion-free sheaves involves significantly more technical machinery, and so this has been deferred to a future publication [16].…”

Section: Moduli Spaces Of Equivariant Torsion-free Sheavesmentioning

confidence: 99%

“…Each isotypic component of an A-module M , where both A and M have T actions compatible with the ring action, is a module over the weight zero part of A. In the cases relevant here, the weight zero part of the ring will always be the field C. A module over a field is precisely a vector space, thus each isotypic component of the module is a vector space 16. Usually one states a sheaf is torsion-free when each stalk is torsion-free, meaning, when each localization of the module is torsion-free.…”

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confidence: 99%

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Sheaves on toric varieties for physics

Knutson¹,

Sharpe²

1998

Advances in Theoretical and Mathematical Physics

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In this paper we give an inherently toric description of a special class of sheaves (known as equivariant sheaves) over toric varieties, due in part to A. A. Klyachko. We apply this technology to heterotic compactifications, in particular to the (0,2) models of Distler, Kachru, and also discuss how knowledge of equivariant sheaves can be used to reconstruct information about an entire moduli space of sheaves. Many results relevant to heterotic compactifications previously known only to mathematicians are collected here -for example, results concerning whether the restriction of a stable sheaf to a Calabi-Yau hypersurface remains stable are stated. We also describe substructure in the Kähler cone, in which moduli spaces of sheaves are independent of Kähler class only within any one subcone. We study F theory compactifications in light of this fact, and also discuss how it can be seen in the context of equivariant sheaves on toric varieties. Finally we briefly speculate on the application of these results to (0,2) mirror symmetry.

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Section: Discussionmentioning

confidence: 99%

“…How can this map be seen in the present language? First, note that the sheaf compatibility conditions in equation (16)…”

Section: Torsion-free Sheaves On Smooth Toric Varietiesmentioning

confidence: 99%

“…To describe moduli spaces of equivariant torsion-free sheaves involves significantly more technical machinery, and so this has been deferred to a future publication [16].…”

Section: Moduli Spaces Of Equivariant Torsion-free Sheavesmentioning

confidence: 99%

mentioning

confidence: 99%

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