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Abstract: In this paper, we study the deformation theory of degenerate algebraic curveson singular varieties which appear as the degenerate limit of families ofvarieties. For this purpose, we systematically develop a new method tocalculate the obstruction cohomology class of degenerate algebraic curves. Thisenables us to judge whether a given degenerate curve can be deformed to asmooth curve or not in variety of situations. In this paper, we apply it tocurves of genus one on degeneration of toric varieties. In particular, weobtain the necessary and sufficient condition for the realizability of tropicalcurves of genus one, extending various results obtained so far.



Autor: Takeo Nishinou

Fuente: https://arxiv.org/



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