Related papers: On the volume of a line bundle

For $k \in \mathbb{Z}_{>0}$, let $\mathcal{H}^{(k)}_{g,n}$ denote the vector bundle over $\mathfrak{M}_{g,n}$ whose every fiber consists of meromorphic $k$-differentials with poles of order at most $k-1$ on a fixed Riemman surface of genus…

In this short note we prove that a Kahler manifold with lower Ricci curvature bound and almost maximal volume is Gromov-Hausdorff close to the projective space with the Fubini-Study metric. This is done by combining the recent results of…

We show that for optical cavities with any finite dissipation, the term "cavity mode" should be understood as a solution to the Helmholtz equation with outgoing wave boundary conditions. This choice of boundary condition renders the problem…

We consider a compact hyperbolic tetrahedron of a general type. It is a convex hull of four points called vertices in the hyperbolic space $\mathbb{H}^3$. It can be determined by the set of six edge lengths up to isometry. For further…

For three dimensional complete, non-compact Riemannian manifolds with non-negative Ricci curvature and uniformly positive scalar curvature, we obtain the sharp linear volume growth ratio and the corresponding rigidity.

We show that the complex projective space has maximal degree (volume) among all n-dimensional Kahler-Einstein Fano manifolds admitting a holomorphic C^*-action with a finite number of fixed points. The toric version of this result,…

The holomorphic invariants introduced by Futaki as obstruction to the asymptotic Chow semistability are studied by an algebraic-geometric point of view and are shown to be the Mumford weights of suitable line bundles on the Hilbert scheme.…

We study a system of equations on a compact complex manifold, that couples the scalar curvature of a Kaehler metric with a spectral function of a first-order deformation of the complex structure. The system comes from an…

We place the representation variety in the broader context of abelian and nonabelian cohomology. We outline the equivalent constructions of the moduli spaces of flat bundles, of smooth integrable connections, and of holomorphic integrable…

We show that a compact Kahler manifold admitting a nondegenerate holomorphic 2-form valued in a line bundle is a finite cyclic cover of a hyperkahler manifold. With respect to the connection induced by the locally hyperkahler metric, the…

Starting with a `bare' 4-dimensional differential manifold as a model of spacetime, we discuss the options one has for defining a volume element which can be used for physical theories. We show that one has to prescribe a scalar density…

Using the techniques of J.-P. Demailly and Th. Peternell in math.AG/0208021 a weak version of Kawamata-Viehweg vanishing is proven for pseudo-effective line bundles on compact Kaehler manifolds. It is a weak version, since one has to adjust…

Let $(X,\omega)$ be a compact K\"ahler manifold. We prove the existence and uniqueness of solutions to complex Monge-Amp\`ere equations with prescribed singularity type. Compared to previous work, the assumption of small unbounded locus is…

We determine putative optimal packings of regular spherical polygons via optimization on smooth manifolds. For several cases, we establish maximality by extending the Lov\'asz theta number to Cayley graphs on the special orthogonal group…

This paper primarily establishes an asymptotic variance estimate for smooth linear statistics associated with zero sets of systems of random holomorphic sections in a sequence of positive Hermitian holomorphic line bundles on a compact…

We study the harmonic space of line bundle valued forms over a covering manifold with a discrete group action $\Gamma$, and obtain an asymptotic estimate for the $\Gamma$-dimension of the harmonic space with respect to the tensor times $k$…

We study some canonical differential operators on vector bundles over smooth, complete Riemannian manifolds. Under very general assumptions, we show that smooth, compactly supported sections are dense in the domains of these operators.…

We show that any big line bundle on a smooth projective variety admits a special Fujita approximation: the volume and the first Riemann-Roch coefficient are both approximated by those of ample $\mathbb{Q}$-line bundles on higher models.…

We extend the well-known formula for the Euler class of a real oriented even-dimensional vector bundle in terms of the curvature of a metric connection to the case of a general linear connection provided a metric is present. We rewrite the…

We consider heterotic E8xE8 supergravity compactified on smooth Calabi-Yau manifolds with line bundle gauge backgrounds. Infinite sets of models that satisfy the Bianchi identities and flux quantization conditions can be constructed by…