相关论文: Trihyperkahler reduction and instanton bundles on …

We study $H$-instanton bundles on the infinite family of smooth three-dimensional varieties $X_e=\mathbb{P}(\mathcal{O}_{\mathbb{P}^2} \oplus \mathcal{O}_{\mathbb{P}^2}(e))$, for $e \geq 0$. We provide two distinct monadic descriptions of…

Let $X$ be a connected, compact complex manifold and $S\subset X$ a separating real hypersurface, so that $X$ decomposes as a union of compact complex manifolds with boundary $\bar X^\pm$. Let $\mathcal{M}$ be the moduli space of $S$-framed…

We study the symplectic geometry of the moduli spaces $M_r=M_r(\s^3)$ of closed n-gons with fixed side-lengths in the 3-sphere. We prove that these moduli spaces have symplectic structures obtained by reduction of the fusion product of $n$…

This is the third in a series of papers constructing hyperbolic structures on all Haken three-manifolds. This portion deals with the mixed case of the deformation space for manifolds with incompressible boundary that are not acylindrical,…

Recently N.Nekrasov and A.Schwarz proposed a modification of the ADHM construction of instantons which produces instantons on a noncommutative deformation of the 4-dimensional real affine space. In this paper we study the relation between…

The Hermitian symmetric space $M=\mathrm{EIII}$ appears in the classification of complete simply connected Riemannian manifolds carrying a parallel even Clifford structure. This means the existence of a real oriented Euclidean vector bundle…

In the 1980s, Neumann and Zagier introduced a symplectic vector space associated to an ideal triangulation of a cusped 3-manifold, such as a knot complement. We give a geometric interpretation for this symplectic structure in terms of the…

Let $(M,J)$ be a complex manifold of complex dimension $n$. A $p$-K\"ahler structure on $(M,J)$ is a real, closed $(p,p)$-transverse form. In this paper, we address the conjecture of L. Alessandrini and G. Bassanelli on $(n-2)$-K\"ahler…

In this paper we describe a physical realization of a family of non-compact Kahler threefolds with trivial canonical bundle in hybrid Landau-Ginzburg models, motivated by some recent non-Kahler solutions of Strominger systems, and utilizing…

We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…

We prove that all complex analytic subvarieties of a generic compact hyperkaehler manifold are even-dimensional. Moreover, these subvarieties are holomorphically symplectic.

We study the moduli space $\fM^s(6;3,6,4)$ of simple rank 6 vector bundles $\E$ on $\PP^3$ with Chern polynomial $1+3t+6t^2+4t^3$ and properties of these bundles, especially we prove some partial results concerning their stability. We first…

Let $\pi: P\to B$ be a locally trivial fiber bundle over a connected CW complex $B$ with fiber equal to the closed symplectic manifold $(M,\om)$. Then $\pi$ is said to be a symplectic fiber bundle if its structural group is the group of…

This thesis is an investigation of the moduli spaces of instanton bundles on the Fano threefold $Y_5$ (a linear section of $\mathbb{G}r(2,5)$). It contains new proofs of classical facts about lines, conics and cubics on $Y_5$, and about…

In this note we prove that the moduli space of torsion-free modules of rank one over an Azumaya algebra on a K3-surface is an irreducible symplectic variety deformation equivalent to a Hilbert scheme of points on the K3-surface.

We consider the action of symplectic monodromy on chain-level enhancements of quantum cohomology. First, we construct a family version of $A_\infty$-structure on quantum cohomology (this should morally correspond to Hochschild cohomology of…

For a generic anti-canonical hypersurface in each smooth toric Fano 4-fold with rank 2 Picard group, we prove there exist three isolated rational curves in it. Moreover, for all these 4-folds except one, the contractions of generic…

In this article, we derive a topological obstruction to the removal of a isolated degenerate complex tangent to an embedding of a 3-manifold into $\mathbb{C}^3$ (without affecting the structure of the remaining complex tangents). We…

We clarify the undecided case $c_2 = 3$ of a theorem of Ein, Hartshorne and Vogelaar [Math. Ann. 259 (1982), 541--569] about the restriction of a stable rank 3 vector bundle with $c_1 = 0$ on the projective 3-space to a general plane. It…

We show that the nefness of the canonical bundle of compact K\"ahler threefolds is invariant under deformed symplectic diffeomorphisms.