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2 June 2020
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In lockdowns, why do some people stay home, while others violate the quarantine rules and go out for picnics in the park? Behavioural economics may provide the answer to this question. Oksana Zinchenko, a Research Fellow of the Institute of Cognitive Neuroscience, explains how we can predict people’s behaviour with game theory.
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Article

Worst Singularities of Plane Curves of Given Degree

Journal of Geometric Analysis. 2017.
Cheltsov I.
In press

We prove that (Formula presented.) and (Formula presented.) are the smallest log canonical thresholds of reduced plane curves of degree (Formula presented.), and we describe reduced plane curves of degree d whose log canonical thresholds are these numbers. As an application, we prove that (Formula presented.) and (Formula presented.) are the smallest values of the (Formula presented.)-invariant of Tian of smooth surfaces in (Formula presented.) of degree (Formula presented.). We also prove that every reduced plane curve of degree (Formula presented.) whose log canonical threshold is smaller than (Formula presented.) is GIT-unstable for the action of the group (Formula presented.), and we describe GIT-semistable reduced plane curves with log canonical thresholds (Formula presented.).

Language: English
DOI
Keywords: $$\alpha $$α-Invariant of TianGIT-stabilityLog canonical thresholdplane curvesSmooth surface
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Added: Sep 13, 2018
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