Related papers: Lifting Weighted Blow-ups

Let X denote a reduced algebraic variety and D a Weil divisor on X. The pair (X,D) is said to be semi-simple normal crossings (semi-snc) at a point a of X if X is simple normal crossings at a (i.e., a simple normal crossings hypersurface,…

We consider two compacta with minimal non-elementary convergence actions of a countable group. When there exists an equivariant continuous map from one to the other, we call the first a blow-up of the second and the second a blow-down of…

A smooth scheme X over a field k of positive characteristic is said to be strongly liftable over W_2(k), if X and all prime divisors on X can be lifted simultaneously over W_2(k). In this paper, we first deduce the Kummer covering trick…

We generalize type $A$ quivers to continuous type $A$ quivers and prove initial results about pointwise finite-dimensional (pwf) representations. We classify the indecomosable pwf representations and provide a decomposition theorem,…

Given a submanifold Z inside X, let Y be the blow-up of X along Z. When the normal bundle of Z in X is convex with a minor assumption, we prove that genus-zero GW-invariants of Y with cohomology insertions from X, are identical to…

In this paper we extend to the singular setting the theory of Fano foliations developed in our previous paper. A Q-Fano foliation on a complex projective variety X is a foliation F whose anti-canonical class is an ample Q-Cartier divisor.…

Consider a compact symplectic sub-orbifold groupoid $\sf S$ of a compact symplectic orbifold groupoid $(\mathsf X,\omega)$. Let $\mathsf X_{\mathfrak a}$ be the weight-$\mathfrak a$ blowup of $\sf X$ along $\sf S$, and $\mathsf D_{\mathfrak…

In the paper [MTT] a conceptuel description of compactifications of moduli spaces of stable vector bundles on surfaces has been given, whose boundaries consist of vector bundles on trees of sufaces. In this article a typical basic case for…

This article shall serve as a quick reference for somebody who needs precise information on concepts and results related to resolution of singularities. As such, it is more a technical manual than a bedtime story. Topics which are covered:…

Let X be a compact Moishezon manifold which becomes projective after blowing up a smooth subvariety $Y \subset X$. We assume also that there exists a proper map $\rho :X \to X'$ onto a projective variety X' with $\rho(Y)$ a point, such that…

An asymptotic formula for the Tian-Paul CM-line of a flat family blown-up at a flat closed sub-scheme is given. As an application we prove that the blow-up of a polarized manifold along a (relatively) Chow-unstable submanifold admits no…

The strong factorization conjecture states that a proper birational map between smooth algebraic varieties over a field of characteristic zero can be factored as a sequence of smooth blowups followed by a sequence of smooth blowdowns. We…

Blowing up a point p in a manifold M builds a new manifold M' in which p is replaced by the projectivization of the tangent space of M at p. This well-known operation also applies to fixed points of diffeomorphisms, yielding continuous…

We investigate the triangle singularity $f=x^a+y^b+z^c$, or $S=k[x,y,z]/(f)$, attached to a weighted projective line $X$ given by the weight triple $(a,b,c)$. We investigate the stable category of vector bundles on $X$ obtained from the…

In [1] some quotients of one-parameter families of Calabi-Yau varieties are related to the family of Mirror Quintics by using a construction due to Shioda. In this paper, we generalize this construction to a wider class of varieties. More…

Theorem: If W is a smooth complex projective variety with h^1 (O-script_W) = 0, then a sufficiently ample smooth divisor X on W cannot be a hyperplane section of a Calabi-Yau variety, unless W is itself a Calabi-Yau. Corollary: A smooth…

We show that the blow-up of a generalized Kahler 4-manifold in a nondegenerate complex point admits a generalized Kahler metric. As with the blow-up of complex surfaces, this metric may be chosen to coincide with the original outside a…

We extend some results of [BF12] on subfactor projections to show that the projection of a free factor B to the free factor complex of the free factor A is well-defined with uniformly bound diameter, unless either A is contained in B or A…

Let $\mathbb{F}_q$ be a finite field with $q$ elements, $\psi$ a non-zero element of $\mathbb{F}_q$, and $n$ an integer $\geq 3$ prime to $q$. The aim of this article is to show that the zeta function of the projective variety over…

In this note, given a pair $(\mathfrak{g}, \lambda)$, where $\mathfrak{g}$ is a complex semisimple Lie algebra and $\lambda \in \mathfrak{h}^*$ is a dominant integral weight of $\mathfrak{g}$, where $\mathfrak{h} \subset \mathfrak{g}$ is…