Related papers: A minimal regularity for the area formula in the E…

In this paper, we study the blow-up analysis of an affine Toda system corresponding to minimal surfaces into ${\mathbb S}^4$ [19]. This system is an integrable system which is a natural generalization of sinh-Gordon equation [18]. By…

Support $\tau$-tilting modules correspond to some classes of categorical objects bijectively, such as two-term tilting complexes for any finite dimensional symmetric algebra. This fact motivates us to classify support $\tau$-tilting modules…

We carry out the complete group classification of the class of (1+1)-dimensional linear Schr\"odinger equations with complex-valued potentials. After introducing the notion of uniformly semi-normalized classes of differential equations, we…

We prove that for any $d>0$ there exists an embedding of the Riemann sphere $\mathbb P^1$ in a smooth complex surface, with self-intersection $d$, such that the germ of this embedding cannot be extended to an embedding in an algebraic…

We prove that the fundamental group of the group of Hamiltonian diffeomorphisms of the symplectic manifold that is obtain by blowing up a submanifold contains an element of infinite order. We prove this using Weinstein's morphism and by…

We investigate the Brauer group of the ring $\mathcal{O}(S)$ of holomorphic functions on a finite-dimensional Stein space S. We provide a purely topological computation of this group and deduce a comparison theorem between the \'etale…

Assuming projective determinacy, we extend Spector's strong version of the Spector-Gandy Theorem to all odd levels of the projective hierarchy: Theorem. For every space $X$ which is a finite product of the natural numbers $N$ and Baire…

We prove lifting theorems for complex representations $V$ of finite groups $G$. Let $\sigma=(\sigma_1,\dots,\sigma_n)$ be a minimal system of homogeneous basic invariants and let $d$ be their maximal degree. We prove that any continuous map…

Let $S$ be a smooth projective surface, and $\hat{S}$ be its blow-up at a point. In this paper, we study the derived category of the Hilbert scheme of points on the blow-up $\hat{S}$. We obtain a semi-orthogonal decomposition consisting of…

This is the first part of two papers. In this part, we prove the blowup formulae for virtual Hodge polynomials of Gieseker moduli spaces of rank-2 stable sheaves and Uhlenbeck compactification spaces over algebraic surfaces. In particular,…

In this article, I prove the following statement: Every compact complex surface with even first Betti number is deformation equivalent to one which admits an extremal K\"ahler metric. In fact, this extremal K\"ahler metric can even be taken…

We show that for every $\alpha > 0$, there exist $n$-point metric spaces (X,d) where every "scale" admits a Euclidean embedding with distortion at most $\alpha$, but the whole space requires distortion at least $\Omega(\sqrt{\alpha \log…

Let $\Gamma$ be either i) the absolute Galois group of a local field $F$, or ii) the topological fundamental group of a closed connected orientable surface of genus $g$. In case i), assume that $\mu_{p^2} \subset F$. We give an elementary…

We define an analytic index and prove a topological index theorem for a non-compact manifold $M\_0$ with poly-cylindrical ends. We prove that an elliptic operator $P$ on $M\_0$ has an invertible perturbation $P+R$ by a lower order operator…

We compute the entropy of systems of quantum particles satisfying the fractional exclusion statistics in the space-time of 2+1 dimensional black hole by using the brick-wall method. We show that the entropy of each effective quantum field…

If $\alpha_1,\ldots,\alpha_r$ are algebraic numbers such that $$N=\sum_{i=1}^r\alpha_i \ne \sum_{i=1}^r\alpha_i^{-1}$$ for some integer $N$, then a theorem of Beukers and Zagier gives the best possible lower bound on $$\sum_{i=1}^r\log…

We consider the 3-point blow-up of the manifold $ (S^2 \times S^2, \sigma \oplus \sigma)$ where $\sigma$ is the standard symplectic form which gives area 1 to the sphere $S^2$, and study its group of symplectomorphisms $\rm{Symp} ( S^2…

In this new version, we give an affirmative solution to a conjecture of Cheng proposed in 1979 which asserts that the Bergman metric of a smoothly bounded strongly pseudoconvex domain in $\mathbb{C}^n, n\geq 2,$ is K\"ahler-Einstein if and…

For the cyclic group $C_2$ we give a complete description of the derived category of perfect complexes of modules over the constant Mackey ring $\underline{\mathbb{Z}/\ell}$, for $\ell$ a prime. This is fairly simple for $\ell$ odd, but for…

The first main result is a topological rigidity theorem for complete immersed hypersurfaces of spherical space forms which extends similar results due to do Carmo/Warner, Wang/Xia and Longa/Ripoll. Under certain sharp conditions on the…