Related papers: Expected Euler characteristic of excursion sets of…

For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most basic intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth…

We characterise high-dimensional topology that arises from a random Cech complex constructed on the circle. Expected Euler characteristic curve is computed, where we observe limiting spikes. The spikes correspond to expected Betti numbers…

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula for the cardinality of the colimit of a diagram of sets is proved,…

We give a self contained proof using Seiberg Witten invariants that for K\"ahler surfaces with non negative Kodaira dimension (including those with $p_g = 0$) the canonical class of the minimal model and the $(-1)$-curves, are oriented…

We deal with compact Kaehler manifolds M which are acted on by a semisimple compact Lie group G of isometries with codimension one regular orbits. We provide an explicit description of the standard blow-ups of such manifolds along complex…

For $m\geq n$, Let $K$ be an algebraic closed base field, and define $\tau_{m,n,k}$ to be the set of $m\times n$ matrices over $K$ with kernel dimension $\geq k$. This is a projective subvariety of $\mathbb{P}^{mn-1}$, and is usually called…

In this paper, we examine the performance of randomised Euler-Maruyama (EM) method for additive time-inhomogeneous SDEs with an irregular drift. In particular, the drift is assumed to be $\alpha$-H\"older continuous in time and bounded…

We establish here a Quantitative Central Limit Theorem (in Wasserstein distance) for the Euler-Poincar\'{e} Characteristic of excursion sets of random spherical eigenfunctions in dimension 2. Our proof is based upon a decomposition of the…

Let M be a compact smooth manifold of dimension n with or without boundary, and f : M $\rightarrow$ R be a smooth Gaussian random field. It is very natural to suppose that for a large positive real u, the random excursion set {f $\ge$ u} is…

Obstruction flatness of a strongly pseudoconvex hypersurface $\Sigma$ in a complex manifold refers to the property that any (local) K\"ahler-Einstein metric on the pseudoconvex side of $\Sigma$, complete up to $\Sigma$, has a potential…

We study random surfaces constructed by glueing together $N/k$ filled $k$-gons along their edges, with all $(N-1)!! = (N-1)(N-3)...3\cdot 1$ pairings of the edges being equally likely. (We assume that lcm $\{2,k\}$ divides $N$.) The Euler…

Let $Y$ be a compact complex manifold embedded in a complex manifold with unitary flat normal bundle. Our interest is in a sort of the linearizability problem of a neighborhood of $Y$. As a higher-codimensional generalization of Ueda's…

We study the asymptotic properties of the conormal cycle of nodal sets associated to a random superposition of eigenfunctions of the Laplacian on a smooth compact Riemannian manifold without boundary. In the case where the dimension is odd,…

In this article we investigate Hirzebruch-Riemann-Roch formulae for line bundles on irreducible symplectic K\"ahler manifolds. As Huybrechts has shown, for every irreducible complex K\"ahler manifold $X$ of dimension $2n$, there are numbers…

In this paper, we study the regular quantizations of K\"{a}hler manifolds by using the first two coefficients of Bergman function expansions. Firstly, we obtain sufficient and necessary conditions for certain Hermitian holomorphic vector…

In this paper, we study the relation between the existence of a negatively (holomorphically) pinched K\"ahler metric on a complex manifold $M$ and its disc bundle contained in a Hermitian line bundle over $M$.

Suppose that we have a compact K\"ahler manifold $X$ with a very ample line bundle $\mathcal{L}$. We prove that any positive definite hermitian form on the space $H^0 (X,\mathcal{L})$ of holomorphic sections can be written as an $L^2$-inner…

Following H. Tomita and C. Murakami we propose an analytical model to predict critical probability of percolation. It is based on the excursion set theory which allows us to consider N-dimensional bounded regions. Details are given for the…

We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a certain…

The authors give a short survey of previous results on $\delta$-homogeneous Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with non-negative sectional curvature, which properly includes the class of all normal…