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- W2160740909 abstract "We prove a new patchworking theorem for singular algebraic curves, which states the following. Given a complex toric threefold $Y$ which fibers over ${mathbb C}$ with a reduced reducible zero fiber $Y_0$ and other fibers $Y_t$ smooth, and given a reduced curve $C_0subset Y_0$, the theorem provides a sufficient condition for the existence of a one-parametric family of curves $C_tsubset Y_t$, which induces an equisingular deformation for some singular points of $C_0$ and certain prescribed deformations for the other singularities. As application we give a comment on a recent theorem by G. Mikhalkin on enumeration of nodal curves on toric surfaces via non-Archimedean amoebas [arXiv:math.AG/0209253]. Namely, using our patchworking theorem, we establish link between nodal curves over the field of complex Puiseux series and their non-Archimedean amoebas, what has been done by Mikhalkin in a different way. We discuss also the case of curves with a cusp as well as real nodal curves." @default.
- W2160740909 created "2016-06-24" @default.
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- W2160740909 date "2002-11-18" @default.
- W2160740909 modified "2023-10-15" @default.
- W2160740909 title "Patchworking singular algebraic curves, non-Archimedean amoebas and enumerative geometry" @default.
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