scholarly journals Gorenstein stable surfaces with $K_X^2 = 2$ and $\chi(\mathcal O_X) = 4$

Author(s):  
Ben Anthes
Keyword(s):  
2021 ◽  
pp. 2150097
Author(s):  
Vicente Lorenzo

Minimal algebraic surfaces of general type [Formula: see text] such that [Formula: see text] are called Horikawa surfaces. In this note, [Formula: see text]-actions on Horikawa surfaces are studied. The main result states that given an admissible pair [Formula: see text] such that [Formula: see text], all the connected components of Gieseker’s moduli space [Formula: see text] contain surfaces admitting a [Formula: see text]-action. On the other hand, the examples considered allow us to produce normal stable surfaces that do not admit a [Formula: see text]-Gorenstein smoothing. This is illustrated by constructing non-smoothable normal surfaces in the KSBA-compactification [Formula: see text] of Gieseker’s moduli space [Formula: see text] for every admissible pair [Formula: see text] such that [Formula: see text]. Furthermore, the surfaces constructed belong to connected components of [Formula: see text] without canonical models.


1998 ◽  
Vol 72 (16) ◽  
pp. 2035-2037 ◽  
Author(s):  
Wu Ting ◽  
N. Koshizuka ◽  
S. Tanaka

Perception ◽  
1984 ◽  
Vol 13 (5) ◽  
pp. 547-553
Author(s):  
James Thomas Enright

When the dynamic visual noise of an untuned television set is viewed with image defocusing (positive lenses) and with a narrow vertical obstruction partially blocking the pupil of one eye, the video ‘snow’ seems to separate into two stable surfaces at different depths, divided by a vertical discontinuity. The main features of this illusion can be quantitatively accounted for in terms of the optics of defocused images and the retinal disparities predicted from blur circles. A residual component of the illusion, however, which was perceived by a majority of subjects, cannot be readily explained by geometrical optics; it apparently reflects a more subtle aspect in the processing of visual images, corresponding to the Anstis–Howard–Rogers stereo-effect, in which local depth configurations can bias global stereopsis. Several novel aspects of that effect are described, based on use of this obstructed-pupil illusion as the evoking stimulus.


2017 ◽  
Vol 28 (04) ◽  
pp. 1750021 ◽  
Author(s):  
Julie Rana

We give a bound on which singularities may appear on Kollár–Shepherd-Barron–Alexeev stable surfaces for a wide range of topological invariants and use this result to describe all stable numerical quintic surfaces (KSBA-stable surfaces with [Formula: see text]) whose unique non-Du Val singularity is a Wahl singularity. We then extend the deformation theory of Horikawa to the log setting in order to describe the boundary divisor of the moduli space [Formula: see text] corresponding to these surfaces. Quintic surfaces are the simplest examples of surfaces of general type and the question of describing their moduli is a long-standing question in algebraic geometry.


2018 ◽  
Vol 6 (35) ◽  
pp. 16731-16768 ◽  
Author(s):  
Xueshan Jing ◽  
Zhiguang Guo

A detailed introduction to superhydrophobic surfaces with superior durability characteristics and comprehensive discussion about fabrication approaches to prolong surface lifetimes are presented in this review, which is expected to inspire a number of scholars to fabricate more durable superhydrophobic materials.


2019 ◽  
Vol 7 (3) ◽  
pp. 215 ◽  
Author(s):  
Levent Tanyeri ◽  
Sercan Öncen

Purpose: Snowboarding is a branch of sport, an individual Alpine sport, which requires superior physical structure. In snowboarding, snowboarders are expected to have high level aerobic and anaerobic strength to become successful. In the present study, the effects of training programs on different surfaces on slalom downhill speed of snowboarding-Alpine snowboarders were examined.Methods: 18 male snowboarders in the Turkish National Snowboarding Alpine team participated in the study. Snowboarders were divided into two groups. Experimental group (G1) was divided into train on non-stable surface and stable surface groups. The experimental group got a coordination and classical snowboarding training program on different surfaces over 8 weeks for 2 days per week (Tuesday-Thursday). Stable surfaces were used on Tuesday and consisted of surfaces with Bosu ball, balance rope, plates ball, balance cushion, balance board, and balance disk. Non-stable surfaces were used on Wednesday and consisted foo skiing exercises that will disturb the balance of the sport player including straight slalom track, degrade surface track, skiing on hard surface, skiing on soft surface, skiing on one foot with eyes open, skiing with eyes closed. The control group (CG) received a classical training program. Trainings were scheduled to leave at least 36 hours between two application days. To determine the speed capacities of the snowboarders the slalom downhill speed test was used; to test agility, the hexagonal test was used, and to measure balance techno body prokin static and dynamic balance tests were used. In the data analysis, descriptive statistics were used. For comparative analysis, the Mann-Whitney U test was used and the significance level was selected as 0.05.Findings: The research results revealed that coordination trainings conducted on different surfaces for 8 weeks had a significant effect on slalom downhill speed of snowboarding-Alpine snowboarders.


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