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We study the Morse theory of the Yang-Mills-Higgs functional on the space of pairs (A, Φ), where A is a unitary connection on a rank 2 hermitian vector bundle over a compact Riemann surface, and Φ is ...
Direct calculation of higher rank invariants of stable pairs using the Joyce machinery of stack functions
higher rank invariants Direct calculation Joyce machinery stack functions
2011/8/23
Abstract: The rank 2 invariants of stable pairs over a Calabi-Yau threefold were computed in (arXiv:1101.2252) using the wall-crossing formula of Joyce-Song and Kontsevich-Soibelman. The computations ...
Higher rank stable pairs and virtual localization
Higher rank stable pairs virtual localization
2010/12/27
We introduce a higher rank analog of the Pandharipande-Thomas theory of stable pairs on a Calabi-Yau threefold $X$. More precisely, we develop a moduli theory for frozen triples given by the data $O^...
Descendent theory for stable pairs on toric 3-folds
Descendent theory stable pairs toric 3-folds
2010/11/23
We prove the rationality of the descendent partition function for stable pairs on nonsingular toric 3-folds. The method uses a geometric reduction of the 2- and 3-leg descendent vertices to the 1-leg...
Let $(X,\mathcal{O}_X(1))$ be a polarized smooth projective variety over the complex numbers. Fix $\mathcal{D}\in \mathrm{coh}(X)$ and a nonnegative rational polynomial $\delta$. Using GIT we contruct...