Related papers: Semipositive line bundles and (1,1)-classes
We construct infinitely many examples of macroscopically large manifolds of dimension $m \geq 4$ equipped with circle bundles whose total spaces admit metrics of positive scalar curvature and have macroscopic dimension at most $\lceil m/2…
We construct symplectic surface bundles over surfaces with positive signatures for all but 18 possible pairs of fiber and base genera. Meanwhile, we determine the commutator lengths of a few new mapping classes.
We classify all closed 1-connected manifolds $M$ which look like projective planes, i.e. with integral homology $H_*(M)=Z^3$. Furthermore, we give an explicit construction of these manifolds as Thom spaces of open disk bundles.
This is a survey article on recent results on vector bundles on symmetric product of non-singular projective curves.
We study PL bordism theories from a quantitative perspective. Such theories include those of PL manifolds, ordinary homology theory, as well as various more exotic theories such as bordism of Witt spaces. In all these cases we show that a…
We study the dynamics of M-theory on G2 holonomy manifolds, and consider in detail the manifolds realized as the quotient of the spin bundle over S^3 by discrete groups. We analyse, in particular, the class of quotients where the triality…
In this preprint the notion of deformation quantization of endomorphism bundles over symplectic manifolds is defined and developed, including index theory.
For any infinite-type surface $S$, a natural question is whether the homology of its mapping class group contains any non-trivial classes that are supported on (i) a compact subsurface or (ii) a finite-type subsurface. Our purpose here is…
We equate dynamical properties (e.g., positive entropy, existence of a periodic curve) of complex projective surface automorphisms with properties of the pull-back actions of such automorphisms on line bundles. We use the properties of the…
The paper presents a classification theorem for the class of flat connections with triangular (0,1)-components on a topologically trivial complex vector bundle over a compact Kahler manifold. As a consequence we obtain several results on…
We survey old and new results on the existence of moduli spaces of semistable coherent sheaves both in algebraic and in complex geometry.
Let $M_1$ and $M_2$ be closed connected orientable $3$-manifolds. We classify the sets of smooth and piecewise linear isotopy classes of embeddings $M_1\sqcup M_2\rightarrow S^6$.
A theory of characteristic classes of vector bundles and smooth manifolds plays an important role in the theory of smooth manifolds. An investigation of reasonable notions of characteristic classes of singular spaces started since a…
We study relations among characteristic classes of smooth manifold bundles with highly-connected fibers. For bundles with fiber the connected sum of $g$ copies of a product of spheres $S^d \times S^d$ and an odd $d$, we find numerous…
We provide supplements and open problems related to structure theorems for maximal rationally connected fibrations of certain positively curved projective varieties, including smooth projective varieties with semi-positive holomorphic…
In this note we identify two complex structures (one is given by algebraic geometry, the other by gauge theory) on the set of isomorphism classes of holomorphic bundles with section on a given compact complex manifold. In the case of line…
In this paper we study the question of whether on smooth projective surfaces the denominators in the volumes of big line bundles are bounded. In particular we investigate how this condition is related to bounded negativity (i.e., the…
A semiholomorphic foliations of type (n, d) is a differentiable real manifold X of dimension 2n + d, foliated by complex leaves of complex dimension n. In the present work, we introduce an appropriate notion of pseudoconvexity (and…
We prove the existence of positive solutions for a class of semipositone problem with singular Trudinger-Moser nonlinearities. The proof is based on compactness and regularity arguments.
We show that the prequantum line bundle on the moduli space of flat $SU(2)$ connections on a closed Riemann surface of positive genus has degree 1. It then follows from work of Lawton and the second author that the classifying map for this…