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http://bura.brunel.ac.uk/handle/2438/29647| Title: | Lowest log canonical thresholds of a reduced plane curve of degree d |
| Other Titles: | Lowest log canonical thresholds of a reduced plane curve of degree <i>d</i> |
| Authors: | Viswanathan, N |
| Keywords: | log canonical threshold;plane curves;α-invariant of Tian singularity |
| Issue Date: | 27-Oct-2019 |
| Publisher: | Springer Nature |
| Citation: | Viswanathan, N. (2020) 'Lowest log canonical thresholds of a reduced plane curve of degree d', European Journal of Mathematics, 2020, 6 (4), pp. 1216 - 1235. doi: 10.1007/s40879-019-00374-z. |
| Abstract: | We describe the sixth worst singularity that a plane curve of degree d⩾ 5 could have, using its log canonical threshold at the point of singularity. This is an extension of a result due to Cheltsov (J Geom Anal 27(3):2302–2338, 2017) wherein the five lowest values of log canonical thresholds of a plane curve of degree d⩾ 3 were computed. These six small log canonical thresholds, in order, are 2 / d, (2 d- 3 ) / (d- 1 ) 2, (2 d- 1 ) / (d2- d) , (2 d- 5 ) / (d2- 3 d+ 1 ) , (2 d- 3 ) / (d2- 2 d) and (2 d- 7 ) / (d2- 4 d+ 1 ). We give examples of curves with these values as their log canonical thresholds using illustrations. |
| URI: | https://bura.brunel.ac.uk/handle/2438/29647 |
| DOI: | https://doi.org/10.1007/s40879-019-00374-z |
| ISSN: | 2199-675X |
| Appears in Collections: | Dept of Mathematics Research Papers |
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