Abstract
This paper presents a definition of ${\Bbb C}^*$-equivariant degeneration families of compact complex curves over ${\Bbb C}$. Those families are called ${\Bbb C}^*$-pencils of curves. We give the canonical method to construct them and prove some results on relations between them and normal surface singularities with ${\Bbb C}^*$-action. We also define ${\Bbb C}^*$-equivariant degeneration families of compact complex curves over ${\Bbb P}^1$. From this, it is possible to introduce a notion of dual ${\Bbb C}^*$-pencils of curves naturally. Associating it, we prove a duality for cyclic covers of normal surface singularities with ${\Bbb C}^*$-action.
Citation
Tadashi TOMARU. "${\Bbb C}^*$-equivariant degenerations of curves and normal surface singularities with ${\Bbb C}^*$-action." J. Math. Soc. Japan 65 (3) 829 - 885, July, 2013. https://doi.org/10.2969/jmsj/06530829
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