Related papers: Fundamental Groups of Blow-ups

We study relations between reflections in (positive or negative) points in the complex hyperbolic plane. It is easy to see that the reflections in the points q_1,q_2 obtained from p_1,p_2 by moving p_1,p_2 along the geodesic generated by…

We study the universal groups of inverse semigroups associated with point sets and with tilings. We focus our attention on two classes of examples. The first class consists of point sets which are obtained by a cut and projection scheme…

We describe blowups of C^n/Z_n orbifolds as complex line bundles over CP^{n-1}. We construct some gauge bundles on these resolutions. Apart from the standard embedding, we describe U(1) bundles and an SU(n-1) bundle. Both blowups and their…

In this paper we develop a general theory of modules which are invariant under automorphisms of their covers and envelopes. When applied to specific cases like injective envelopes, pure-injective envelopes, cotorsion envelopes, projective…

In terms of the gauged nonlinear $\sigma$-models, we describe some results and implications of solving the following problem: Given a smooth symplectic manifold as target space with a quasi-free Hamiltonian group action, perform the…

We establish a new fundamental class of varieties in nonnoetherian algebraic geometry related to the central geometry of dimer algebras. Specifically, given an affine algebraic variety $X$ and a finite collection of non-intersecting…

Blowing up a rational surface singularity in a reflexive module gives a (any) partial resolution dominated by the minimal resolution. The main theorem shows how deformations of the pair (singularity, module) relates to deformations of the…

In this paper we present a method for extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimension,…

Motivated by the theory of Inoue-type varieties, we give a structure theorem for projective manifolds $W_0$ with the property of admitting a 1-parameter deformation where $W_t$ is a hypersurface in a projective smooth manifold $Z_t$. Their…

We extend the classical formula of Porteous for blowing-up Chern classes to the case of blow-ups of possibly singular varieties along regularly embedded centers. The proof of this generalization is perhaps conceptually simpler than the…

The goal of this paper is to describe the birational geometry of the blowup of $\mathbb{P}^n$ at $n+4$ points in very general position. To achieve this, we follow an idea of Mukai and explore a special instance of Gale duality, namely, a…

Classical invariant theory of a complex reflection group $W$ highlights three beautiful structures: -- the $W$-invariant polynomials constitute a polynomial algebra, over which -- the $W$-invariant differential forms with polynomial…

Let $M$ be a closed manifold that admits a self-cover $p:M \to M$ of degree >1. We say p is strongly regular if all its iterates are regular covers. In this case, we establish an algebraic structure theorem for the fundamental group of $M$:…

We investigate the natural involutive structure on the blow-up of ${\Bbb R}^n$ in ${\Bbb C}^n$ extending the complex structure on the complement of the exceptional hypersurface. Our main result is that this structure is hypocomplex, meaning…

Reflexive polygons have attracted great interest both in mathematics and in physics. This paper discusses a new aspect of the existing study in the context of quiver gauge theories. These theories are 4d supersymmetric worldvolume theories…

Real blow-ups and more refined "zooms" play a key role in the analysis of singularities of complex-analytic differential modules. They do not change the underlying topology, but the uniform structure. This suggests to revisit the cohomology…

We review aspects of an important paper by Robert Strichartz concerning reverse iterated function systems (i.f.s.) and fractal blowups. We compare the invariant sets of reverse i.f.s. with those of more standard i.f.s. and with those of…

Raynaud and Gruson developed the theory of blowing-up an algebraic variety $X$ along a coherent sheaf $M$ in the sense that there exists a blow-up $X'$ of $X$ such that the "strict transform" of $M$ is flat over $X'$ and the blow-up…

Given a real, twisted Dirac structure $L$ on a smooth manifold $M$, and a closed embedded submanifold $N\subseteq M$ of codimension $>1$, we characterise when $L$ lifts to a smooth, twisted Dirac structure on the real projective blowup of…

We show that, in a highest weight category with duality, the endomorphism algebra of a tilting object is naturally a cellular algebra. Our proof generalizes a recent construction of Andersen, Stroppel, and Tubbenhauer. This result raises…