Related papers: Super Gromov-Witten Invariants via torus localizat…
In this paper, we apply recent methods of localized GLSMs to make predictions for Gromov-Witten invariants of noncommutative resolutions, as defined by e.g. Kontsevich, and use those predictions to examine the connectivity of the SCFT…
We show that a holomorphic two-form $\theta$ on a smooth algebraic variety X localizes the virtual fundamental class of the moduli of stable maps $\mgn(X,\beta)$ to the locus where $\theta$ degenerates; it then enables us to define the…
We introduce a geometric completion of the stack of maps from stable marked curves to the quotient stack [point/GL(1)], and use it to construct some gauge-theoretic analogues of the Gromov-Witten invariants. We also indicate the…
We develop a theory of \emph{reduced} Gromov-Witten and stable pair invariants of surfaces and their canonical bundles. We show that classical Severi degrees are special cases of these invariants. This proves a special case of the MNOP…
This survey intends to present the basic notions of Geometric Invariant Theory (GIT) through its paradigmatic application in the construction of the moduli space of holomorphic vector bundles. Special attention is paid to the notion of…
In this thesis I give a new description for the moduli space of stable n pointed curves of genus zero and explicitly specify a natural isomorphism and inverse between them that preserves many important properties. I also give a natural…
Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these integrals from the standard descendent potential…
This paper provides some technical results needed in "Formalism for Relative Gromov-Witten Invariants." We study line-bundles on the moduli stacks of relative stable and rubber maps that are used to define relative Gromov-Witten invariants…
Let $S$ be a projective simply connected complex surface and $\mathcal{L}$ be a line bundle on $S$. We study the moduli space of stable compactly supported 2-dimensional sheaves on the total spaces of $\mathcal{L}$. The moduli space admits…
Seiberg-Witten maps are a well-established method to locally construct noncommutative gauge theories starting from commutative gauge theories. We revisit and classify the ambiguities and the freedom in the definition. Geometrically,…
Let $V$ be a linear representation of a connected complex reductive group $G$. Given a choice of character $\theta$ of $G$, Geometric Invariant Theory defines a locus $V^{ss}_\theta(G) \subseteq V$ of semistable points. We give necessary,…
In this article, we construct the reduced genus-two Gromov-Witten invariants for certain almost K\"{a}hler manifold $(X, \omega, J)$ such that $J$ is integrable and satisfies some regularity conditions. In particular, the standard…
This is the first part of a trilogy where we apply the theory of virtual manifold/orbifolds developed by the first named author and Tian to study the Gromov-Witten moduli spaces. In this paper, we resolve the main analytic issue arising…
We extend B. Hassett's theory of weighted stable pointed curves ([Has03]) to weighted stable maps. The space of stability conditions is described explicitly, and the wall-crossing phenomenon studied. This can be considered as a non-linear…
We introduce and study a notion of invariant intrinsic torsion geometry which appears, for instance, in connection with the Bryant-Salamon metric on the spinor bundle over S^3. This space is foliated by six-dimensional hypersurfaces, each…
The local Euler obstructions and the Euler characteristics of linear sections with all hyperplanes on a stratified projective variety are key geometric invariants in the study of singularity theory. Despite their importance, in general it…
Building upon work of Y. Shalom we give a homological-algebra flavored definition of an induction map in group homology associated to a topological coupling. As an application we obtain estimates of the (co)homological dimension of groups G…
We show that certain naturally arising cones over the main component of a moduli space of $J_0$-holomorphic maps into $P^n$ have a well-defined euler class. We also prove that this is the case if the standard complex structure $J_0$ on…
We examine the logarithmic Gromov-Witten cycles of a toric variety relative to its full toric boundary. The cycles are expressed as products of double ramification cycles and natural tautological classes in the logarithmic Chow ring of the…
In this paper we introduce invariants of semi-free Hamiltonian actions of $S\sp 1$ on compact symplectic manifolds (which satisfy some technical conditions related to positivity) using the space of solutions to certain gauge theoretical…