Related papers: The Donaldson-Thomas invariants under blowups and …
In this paper we consider the $b$-family of equations on the torus $u\_t- u\_{txx}+ (b+1) u u\_x=b u\_x u\_{xx} + u u\_{xxx}$, which for appropriate values of $b$ reduces to well-known models, such as the Camassa-Holm equation or the…
We compute the Donaldson-Thomas invariants for two types of Calabi-Yau 3-folds. These invariants are associated to the moduli spaces of rank-2 Gieseker semistable sheaves. None of the sheaves are locally free, and their double duals are…
We analyse a blow-up sequence of solutions for Liouville type equations involving Dirac measures with "collapsing" poles. We consider the case where blow-up occurs exactly at a point where the poles coalesce. After proving that a…
For a Calabi-Yau 3-fold $X$, we explicitly compute the Donaldson-Thomas type invariant counting pairs $(F, V)$, where $F$ is a zero-dimensional coherent sheaf on $X$ and $V\subset F$ is a two dimensional linear subspace, which satisfy a…
This is the second paper in a series on intrinsic Donaldson-Thomas theory, a framework for studying the enumerative geometry of general algebraic stacks. In this paper, we present the construction of Donaldson-Thomas invariants for general…
The aim of this paper is to study an analog of non-commutative Donaldson-Thomas theory corresponding to the refined topological vertex for small crepant resolutions of toric Calabi-Yau 3-folds. We define the invariants using dimer models…
We study twisted cohomologies with paracompactifying families of supports. The Kunneth theorems, Leray-Hirsch theorems and self-intersection formulae are established. Based on these results, we eventually give explicit expressions of…
Using the u-plane integral of Moore and Witten, we derive a simple expression for the Donaldson invariants of $\Sigma_g \times S^2$, where $\Sigma_g$ is a Riemann surface of genus g. This expression generalizes a theorem of Morgan and Szabo…
We construct and study Donaldson-Thomas invariants counting orthogonal and symplectic objects in linear categories, which are a generalization of the usual Donaldson-Thomas invariants from the structure groups $\mathrm{GL} (n)$ to the…
We prove the crepant resolution conjecture for Donaldson-Thomas invariants of hard Lefschetz CY3 orbifolds, formulated by Bryan-Cadman-Young, interpreting the statement as an equality of rational functions. In order to do so, we show that…
We prove transformation formulae for generating functions of Gromov-Witten invariants on general toric Calabi-Yau threefolds under flops. Our proof is based on a combinatorial identity on the topological vertex and analysis of fans of toric…
In this paper we compute the motivic Donaldson--Thomas invariants for the quiver with one loop and any potential. As the presence of arbitrary potentials requires the full machinery of \hat(\mu)-equivariant motives, we give a detailed…
We study the Donaldson invariants of rational surfaces and their dependence on the chambers in the ample cone. We build on a previous joint paper in which we have expressed the change of the Donaldson invariants on an algebraic surface $S$…
The local Donaldson-Thomas theory of curves is solved by localization and degeneration methods. The results complete a triangle of equivalences relating Gromov-Witten theory, Donaldson-Thomas theory, and the quantum cohomology of the…
We prove new adjunction inequalities for embedded surfaces in four-manifolds with non-negative self-intersection number by using the Donaldson invariants. These formulas are completely analogous to the ones obtained by Ozsv\'ath and Szab\'o…
Neste segundo artigo sobre sistemas Hamiltonianos, apresentamos o metodo da explosao para a determinacao da natureza de pontos fixos (pontos de equilibrio degenerados. Aplicamos o metodo a dois modelos hamiltonianos com um e dois graus de…
The generalized Donaldson-Thomas invariants counting one dimensional semistable sheaves on Calabi-Yau 3-folds are conjectured to satisfy a certain multiple cover formula. This conjecture is equivalent to Pandharipande-Thomas's strong…
We provide a detailed numerical study of various issues pertaining to the dynamics of the Burgers equation perturbed by a weak dispersive term: blow-up in finite time versus global existence, nature of the blow-up, existence for "long"…
Kontsevich and Soibelman defined the Donaldson-Thomas invariants of a 3d Calabi-Yau category with a stability condition. Any cluster variety can produce an example of such a category, whose corresponding Donaldson-Thomas invariants are…
We apply results on inducing stability conditions to local Calabi-Yau threefolds and obtain applications to Donaldson-Thomas (DT) theory. A basic example is the total space of the canonical bundle of $Z=\mathbb{P}^1\times \mathbb{P}^1$. We…