Related papers: Donaldson Thomas invariant of P^1 scroll

A singular point of a smooth map F: M -> N of manifolds is a point in M at which the rank of the differential dF is less than the minimum of dimensions of M and N. The classical invariant of the set S of singular points of F of a given type…

We study the cohomological properties of the fixed locus $X^G$ of an automorphism group $G$ of prime order $p$ acting on a variety $X$ whose integral cohomology is torsion-free. We obtain an precise relation between the mod $p$ cohomology…

We relate Pandharipande-Thomas stable pair invariants on Calabi-Yau 3-folds containing the projective plane with those on the derived equivalent orbifolds via wall-crossing method. The difference is described by generalized Donaldson-Thomas…

The Separatrix Theorem of C. Camacho and P. Sad guarantees the existence of invariant curve (separatrix) passing through the singularity of germ of holomorphic foliation on complex surface, when the surface underlying the foliation is…

Let $E$ be a rank 2, degree $d$ vector bundle over a genus $g$ curve $C$. The loci of stable pairs on $E$ in class $2[C]$ fixed by the scaling action are expressed as products of $\Quot$ schemes. Using virtual localization, the stable pairs…

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…

Closed string theory exhibits an O(D,D) duality symmetry on tori, which in double field theory is manifest before compactification. I prove that to first order in $\alpha'$ there is no manifestly background independent and duality invariant…

In this paper, we study a series of $L^2$-torsion invariants from the viewpoint of the mapping class group of a surface. We establish some vanishing theorems for them. Moreover we explicitly calculate the first two invariants and compare…

We define an simple invariant of an embedded nullhomologous Lagrangian torus and use this invariant to show that many symplectic 4-manifolds have infinitely many pairwise symplectically inequivalent nullhomologous Lagrangian tori. We…

Let $\mathcal{L}$ be a line bundle on a smooth and proper scheme $X$ over $S$. We compute, in the case where $S$ is smooth over a field of characteristic $0$, the virtual fundamental class of the closed subset of $S$ consisting of those…

Continuing the program of math.SG/0012067 and math.SG/0310450, we introduce refinements of the Donaldson-Smith standard surface count which are designed to count nodal pseudoholomorphic curves and curves with a prescribed decomposition into…

A deformed Donaldson-Thomas (dDT) connection is a Hermitian connection of a Hermitian line bundle over a $G_2$-manifold $X$ satisfying a certain nonlinear PDE. This is considered to be the mirror of a (co)associative cycle in the context of…

Let $C$ be a smooth curve embedded in a smooth quasi-projective threefold $Y$, and let $Q^n_C=\textrm{Quot}_n(\mathscr I_C)$ be the Quot scheme of length $n$ quotients of its ideal sheaf. We show the identity…

We give an elementary construction of the tangent-obstruction theory of the deformations of the pair $(X,L)$ with $X$ a reduced local complete intersection scheme and $L$ a line bundle on $X$. This generalizes the classical deformation…

This paper is motivated by the question of how motivic Donaldson--Thomas invariants behave in families. We compute the invariants for some simple families of noncommutative Calabi--Yau threefolds, defined by quivers with homogeneous…

The modular data of a modular category $\mathcal{C}$, consisting of the $S$-matrix and the $T$-matrix, is known to be an incomplete invariant of $\mathcal{C}$. More generally, the invariants of framed links and knots defined by a modular…

We prove wall-crossing formula for categorical Donaldson-Thomas invariants on the resolved conifold, which categorifies Nagao-Nakajima wall-crossing formula for numerical DT invariants on it. The categorified Hall products are used to…

We characterize all orientations of cycles $C$ for which for every fixed $\varepsilon > 0$ there exists a constant $c \geq 1$ such that every digraph $D$ without loops or parallel arcs with $\chi(D) \geq c$ and minimum out-degree at least…

In this paper we prove a toric localization formula in cohomological Donaldson Thomas theory. Consider a -1-shifted symplectic algebraic space with a C* action leaving the -1-shifted symplectic form invariant. This includes the moduli space…

We develope $\mathbb{C}^{\ast}$-equivariant categorical Donaldson-Thomas theory for local surfaces, i.e. the total spaces of canonical line bundles on smooth projective surfaces. We introduce $\mathbb{C}^{\ast}$-equivariant DT categories…