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• W1488392152 abstract "A detailed algebraic-geometric background is presented for the tropical approach to enumeration of singular curves on toric surfaces, which consists of reducing the enumeration of algebraic curves to that of non-Archimedean amoebas, the images of algebraic curves by a real-valued non-Archimedean valuation. This idea was proposed by Kontsevich and recently realized by Mikhalkin, who enumerated the nodal curves on toric surfaces. The main technical tools are a refined tropicalization of one-parametric equisingular families of curves and the patchworking construction of singular algebraic curves. The case of curves with a cusp and the case of real nodal curves are also treated." @default.
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• W1488392152 date "2006-02-20" @default.
• W1488392152 modified "2023-10-15" @default.
• W1488392152 title "A tropical approach to enumerative geometry" @default.
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• W1488392152 doi "https://doi.org/10.1090/s1061-0022-06-00908-3" @default.
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