Abstract
We discuss the Gromov-Witten/Donaldson-Thomas correspondence for 3-folds in both the absolute and relative cases. Descendents in Gromov-Witten theory are conjectured to be equivalent to Chern characters of the universal sheaf in Donaldson-Thomas theory. Relative constraints in Gromov-Witten theory are conjectured to correspond in Donaldson-Thomas theory to cohomology classes of the Hilbert scheme of points of the relative divisor. Independent of the conjectural framework, we prove degree 0 formulas for the absolute and relative Donaldson-Thomas theories of toric varieties.
| Original language | English |
|---|---|
| Pages (from-to) | 1286-1304 |
| Number of pages | 19 |
| Journal | Compositio Mathematica |
| Volume | 142 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2006 |
Keywords
- Donaldson maps
- Gromov-Witten
- Sheaves
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