Related papers: A Weitzenb\"ock formula on Sasakian holomorphic bu…
We consider an extension of the results of S. Bando, R. Kobyashi, G. Tian, and S. T. Yau on the existence of Ricci-flat K\"{a}hler metrics on quasi-projective varieties Y=X\D with \alpha[D]=c_1(X), \alpha >1. The requirement that D admit a…
In \cite{nr} Narasimhan and Ramanan and in \cite{desing}, Seshadri constructed desingularisations of the moduli space $M^{ss}_{_{\text{SL}(2)}}$ of semistable $\SL(2)$-bundles on a smooth projective curve $C$ of genus $g \geq 3$. Seshadri's…
In previous papers we introduced the notion of special Bohr - Sommerfeld lagrangian cycles on a compact simply connected symplectic manifold with integer symplectic form, and presented the main interesting case: compact simply connected…
We classify simply connected compact Sasaki manifolds of dimension $2n+1$ with positive transverse bisectional curvature. In particular, the K\"ahler cone corresponding to such manifolds must be bi-holomorphic to $\C^{n+1}\backslash \{0\}$.…
Natural metric structures on tangent bundles and tangent sphere bundles enclose many important problems, from the topology of the base to the determination of their holonomy. We make here a brief study of the topic. We find the…
We construct smooth bundles with base and fiber products of two spheres whose total spaces have non-vanishing $\hat{A}$-genus. We then use these bundles to locate non-trivial rational homotopy groups of spaces of Riemannian metrics with…
G.W. Mackey's celebrated obstruction theory for projective representations of locally compact groups was remarkably generalized by J. M. G. Fell and R. S. Doran to the wide area of saturated Banach *-algebraic bundles. Analogous obstruction…
We establish a local model for the moduli space of holomorphic symplectic structures with logarithmic poles, near the locus of structures whose polar divisor is normal crossings. In contrast to the case without poles, the moduli space is…
For any asymptotically dynamically convex contact manifold $Y$, we show that $SH_*(W)=0$ is a property independent of the choice of topologically simple (i.e.\ $c_1(W)=0$ and $\pi_{1}(Y)\rightarrow \pi_1(W)$ is injective) Liouville filling…
The heterotic $SU(3)$ system, also known as the Hull--Strominger system, arises from compactifications of heterotic string theory to six dimensions. This paper investigates the local structure of the moduli space of solutions to this system…
We prove that the moduli space of solutions to the PU(2) monopole equations is a smooth manifold of the expected dimension for simple, generic parameters such as (and including) the Riemannian metric on the given four-manifold. In a…
We investigate the formal principle for holomorphic line bundles on neighborhoods of an analytic subset of a complex manifold mainly in the case where it can be realized as an open subset of a compact K\"ahler manifold. Our approach…
In the breakthrough paper [V. Mu\~noz, A Smale-Barden manifold admitting K-contact but not Sasakian structure, 2024, 10.4171/JEMS/1496], it is constructed the first example of a simply connected compact 5-manifold (aka.\ Smale-Barden…
Studied are moduli spaces of self dual or anti-self dual connections on noncommutative 4-manifolds, especially deformation quantization of compact spin Riemannian 4-manifolds and their isometry groups have 2-torus subgroup. Then such moduli…
We study the moduli space of congruence classes of isometric surfaces with the same mean curvature in 4-dimensional space forms. Having the same mean curvature means that there exists a parallel vector bundle isometry between the normal…
We identify a new class of closed smooth manifolds for which there exists a uniform bound on the Lagrangian spectral norm of Hamiltonian deformations of the zero section in a unit cotangent disk bundle, settling a well-known conjecture of…
Models of two-dimensional (2D) traps, with the double-well structure in the third direction, for Bose-Einstein condensate (BEC) are introduced, with attractive or repulsive interactions between atoms. The models are based on systems of…
A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment (saddle connection) joining a pair of…
We give infinite series of groups Gamma and of compact complex surfaces of general type S with fundamental group Gamma such that 1) Any surface S' with the same Euler number as S, and fundamental group Gamma, is diffeomorphic to S. 2) The…
A proof via the Seiberg-Witten moduli space of Donaldson's theorem on smooth 4-manifolds with definite intersection forms.