• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site
Advanced search
HSE University
Advanced search
Higher School of Economics
National Research University
Priority areas
by year
Subject
News
27 January 2021
Glued to Their Screens: How Do Contemporary School Students Use Devices?
2020 has definitely become a year of online learning. Children of all ages, as well as many adults, have had to study remotely. This has allowed researchers to look at education accessibility problems from a new perspective and evaluate how the massive transition to online learning aligns with existing norms and attitudes toward limiting screen time. Nadezhda Knyaginina and Evgenii Puchkov, researchers from the Education Law Laboratory at the HSE Institute of Education talked about their lab’s research on this matter.
25 January 2021
OECD Outlook Examines the Effects of the Pandemic on Science, Technology, and Innovation
Times of Crisis and Opportunity is the title of the OECD Science, Technology and Innovation (STI) Outlook published in January. The document focuses on STI responses to the pandemic while assessing the impact of the COVID-19 crisis on science and technology. Mikhail Gershman, Deputy Director of the Centre of Science, Technology, Innovation and Information Policy, discusses the contribution of the Institute of Statistical Studies and Economics of Knowledge (ISSEK) to the Outlook and discusses some aspects of ISSEK’s long-standing partnership with OECD.
22 January 2021
Global Restructuring: The World Community Prepares to Fight Climate Change
More than a hundred countries have already declared that they see achieving ‘zero emissions with the exception of absorption’ as their main goal in fighting climate change. For Russia, a country that receives significant income from the export of fossil energy resources, the global rejection of hydrocarbons poses great risks. Experts discussed the issue at the research seminar ‘Decarbonization as a Global Trend: Changing the Economic Landscape and Its Importance for Companies’, which was jointly organized by HSE University and the Association of European Businesses.

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
Similar publications
On a conjecture of Tian
Cheltsov I., Ahmadinezhad H. Mathematische Zeitschrift. 2018. Vol. 288. No. 1-2. P. 217-241.

We study Tian’s α-invariant in comparison with the α1-invariant for pairs (Sd,H) consisting of a smooth surface Sd of degree d in the projective three-dimensional space and a hyperplane section H. A conjecture of Tian asserts that α(Sd,H)=α1(Sd,H). We show that this is indeed true for d=4 (the result is well known for d⩽3), and we show that α(Sd,H)<α1(Sd,H) for d⩾8 provided that Sd is general enough. We also construct examples of Sd, for d=6 and d=7, for which Tian’s conjecture fails. We provide a candidate counterexample for S5.

Added: Sep 13, 2018
Log canonical thresholds of certain Fano hypersurfaces
Cheltsov Ivan, Park J., Won J. Mathematische Zeitschrift. 2014. No. 276. P. 51-79.

We study log canonical thresholds on quartic threefolds, quintic fourfolds, and double spaces. As an important application, we show that they have Kähler–Einstein metrics if they are general.

Added: Nov 14, 2013