Related papers: Blow-ups of three-dimensional toric singularities

Looking at the well understood case of log terminal surface singularities, one observes that each of them is the quotient of a factorial one by a finite solvable group. The derived series of this group reflects an iteration of Cox rings of…

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 f: X -> Z be a local, projective, divisorial contraction between normal varieties of dimension n with Q-factorial singularities. Let $Y \subset X$ be a f-ample Cartier divisor and assume that f|Y: Y -> W has a structure of a weighted…

Let $G$ be a connected algebraic group. We study $G$-equivariant extremal contractions whose centre is a codimension three $G$-simply connected orbit. In the spirit of an important result by Kawakita in 2001, we prove that those…

Every three-fold divisorial contraction to a non-Gorenstein point is a weighted blow-up.

Let $(X,o)$ be a germ of a 3-dimensional terminal singularity of index $m\geq 2$. If $(X,o)$ has type cAx/4, cD/3-3, cD/2-2, or cE/2, then assume that the standard equation of $X$ in $\mathbb{C}^4/\mathbb{Z}_m$ is non-degenerate with…

We classify smooth toric Fano varieties of dimension $n\geq 3$ containing a toric divisor isomorphic to $\PP^{n-1}$. As a consequence of this classification, we show that any smooth complete toric variety $X$ of dimension $n\geq 3$ with a…

We describe three-dimensional terminal toric flips. We obtain the complete local description of three-dimensional terminal toric flips.

In this paper we prove the existence of purely log terminal blow-up for Kawamata log terminal singularity and obtain the criterion for a singularity to be weakly exceptional in terms of the exceptional divisor of plt blow-up.

Let $(X,o)$ be a 3-dimensional terminal singularity of type $cD$ or $cE$ defined in $\mathbb{C}^4$ by an equation non-degenerate with respect to its Newton diagram. We show that there is not more than 1 non-rational divisor $E$ over $(X,o)$…

We study the blow-ups X of P3 along a proj. normal curve C. We look for very ample divisor classes on X of low degree, and we study the ideal of the embedding of X. Some result is generalized to higher dimensions.

Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out…

We show that 3-fold terminal flips and divisorial contractions may be factored into a sequence of flops, blow-downs to a smooth curve in a smooth 3-fold or divisorial contractions to points with minimal discrepancies.

This paper classifies toric Fano 3-folds with singular locus { 1/k(1,1,1) } for any positive integer k, building on the work of Batyrev and Watanabe-Watanabe. This is achieved by completing an equivalent problem in the language of Fano…

We establish the first complete classification of finite-time blow-up scenarios for strong solutions to the three-dimensional incompressible Euler equations with surface tension in a bounded domain possessing a closed, moving free boundary.…

Let X be a projective variety with terminal singularities and let L be an ample Cartier divisor on X. We prove that if f is a birational contraction associated to an extremal ray $ R \subset \bar {NE(X)}$ such that R.(K_X+(n-2)L)<0, then f…

In this note we consider the blowing-up X of P^3 along r general points of the anticanonical divisor of a smooth quadric in P^3. Given a complete linear system |L| = |dH - m_1 E_1 -...- m_r E_r| on X, with H the pull-back of a plane in P^3…

In this paper we describe the implementation that led to the counterexamples to the Nash blowup conjectures recently discovered by the authors. We also provide new examples of toric varieties with prescribed singularities that are not…

We study infinite-distance limits in the complex structure moduli space of elliptic Calabi-Yau threefolds. In F-theory compactifications to six dimensions, such limits include infinite-distance trajectories in the non-perturbative open…

Consider the blow-up $X$ of $\mathbb{P}^3$ at 6 points in very general position and the 15 lines through the 6 points. We construct an infinite-order pseudo-automorphism $\phi_X$ on $X$, induced by the complete linear system of a divisor of…