Wall-crossing and invariants of higher rank Joyce-Song stable pairs

Artan Sheshmani

doi:10.1215/ijm/1455203159

Wall-crossing and invariants of higher rank Joyce-Song stable pairs

Artan Sheshmani

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We introduce a higher rank analog of the Joyce-Song theory of stable pairs. Given a nonsingular projective CalabiYau threefold X, we define the higher rank Joyce-Song pairs given by O^⊕rX(−n)→F where F is a pure coherent sheaf with one dimensional support, r >1 and n≫0 is a fixed integer. We equip the higher rank pairs with a Joyce-Song stability condition and compute their associated invariants using the wallcrossing techniques in the category of “weakly” semistable objects.

Original language	English (US)
Pages (from-to)	55-83
Number of pages	29
Journal	Illinois Journal of Mathematics
Volume	59
Issue number	1
DOIs	https://doi.org/10.1215/ijm/1455203159
State	Published - Mar 1 2015
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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AB - We introduce a higher rank analog of the Joyce-Song theory of stable pairs. Given a nonsingular projective CalabiYau threefold X, we define the higher rank Joyce-Song pairs given by O⊕rX(−n)→F where F is a pure coherent sheaf with one dimensional support, r >1 and n≫0 is a fixed integer. We equip the higher rank pairs with a Joyce-Song stability condition and compute their associated invariants using the wallcrossing techniques in the category of “weakly” semistable objects.

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Wall-crossing and invariants of higher rank Joyce-Song stable pairs

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