# Flipping surfaces

@inproceedings{Hacking2013FlippingS, title={Flipping surfaces}, author={Paul Hacking and J. Tevelev and Giancarlo Urz'ua}, year={2013} }

We study semistable extremal threefold neighborhoods following earlier work of Mori, Kollár, and Prokhorov. We classify possible flips and extend Mori’s algorithm for computing flips of extremal neighborhoods of type k2A to more general neighborhoods of type k1A. In fact we show that they belong to the same deformation family as k2A, and we explicitly construct the universal family of extremal neighborhoods. This construction follows very closely Mori’s division algorithm, which we interpret as… Expand

#### 20 Citations

Invariants of deformations of quotient surface singularities

- Mathematics
- 2018

We find all $P$-resolutions of quotient surface singularities (especially, tetrahedral, octahedral, and icosahedral singularities) together with their dual graphs, which reproduces Jan Steven's list… Expand

Antiflips, mutations, and unbounded symplectic embeddings of rational homology balls

- Mathematics
- 2020

The Milnor fibre of a Q-Gorenstein smoothing of a Wahl singularity is a rational homology ball B_{p,q}. For a canonically polarised surface of general type X, it is known that there are bounds on the… Expand

Milnor fibers and symplectic fillings of quotient surface singularities

- Mathematics
- 2015

We determine a one-to-one correspondence between Milnor fibers and minimal symplectic fillings of a quotient surface singularity (up to diffeomorphism type) by giving an explicit algorithm to compare… Expand

Exceptional collections on Dolgachev surfaces associated with degenerations

- Mathematics, Geography
- 2015

Dolgachev surfaces are simply connected minimal elliptic surfaces with $p_g=q=0$ and of Kodaira dimension 1. These surfaces were constructed by logarithmic transformations of rational elliptic… Expand

On Z/3-Godeaux surfaces

- Mathematics
- 2016

We prove that Godeaux--Reid surfaces with torsion group Z/3 have topological fundamental group Z/3. For this purpose, we describe degenerations to stable KSBA surfaces with one 1/4(1,1) singularity,… Expand

On wormholes in the moduli space of surfaces

- Mathematics
- 2021

We study a certain wormholing phenomenon that takes place in the Kollár–Shepherd-Barron–Alexeev (KSBA) compactification of the moduli space of surfaces of general type. It occurs because of the… Expand

Bounds on Wahl singularities from symplectic topology

- Mathematics
- 2017

Let X be a minimal surface of general type with positive geometric genus ($b_+ > 1$) and let $K^2$ be the square of its canonical class. Building on work of Khodorovskiy and Rana, we prove that if X… Expand

On degenerations of Z/2-Godeaux surfaces

- 2020

We compute equations for the Coughlan’s family in [C16] of Godeaux surfaces with torsion Z/2, which we call Z/2-Godeaux surfaces, and we show that it is (at most) 7 dimensional. We classify… Expand

Simple embeddings of rational homology balls and antiflips

- Mathematics
- 2019

Let $V$ be a regular neighborhood of a negative chain of $2$-spheres (i.e. exceptional divisor of a cyclic quotient singularity), and let $B_{p,q}$ be a rational homology ball which is smoothly… Expand

Families of explicit quasi-hyperbolic and hyperbolic surfaces

- Mathematics
- 2018

We construct explicit families of quasi-hyperbolic and hyperbolic surfaces. This is based on earlier work of Vojta, and the recent expansion and generalization of it by the first author. In this… Expand

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