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2007

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/197441

Bounds of the number of rational maps between varieties of general type

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Abstract

We give a bound for the number of rational maps between algebraic varieties of general type under mild hypothesis on the canonical map. We use an idea inspired by Tanabe's work. Instead of attaching a morphism of Hodge structures to a rational map we simply associate to it a piece of the integral Hodge lattice. This procedure does not give an injective map, but by means of a geometric argument, we can estimate the number of maps with the same image.

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https://doi.org/10.1353/ajm.2007.0040

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Geometria biracional, Teoria de Hodge, Superfícies algebraiques

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Birational geometry, Hodge theory, Algebraic surfaces

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Articles publicats en revistes (Matemàtiques i Informàtica)

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NARANJO DEL VAL, Juan Carlos and PIROLA, Gian Pietro. Bounds of the number of rational maps between varieties of general type. American Journal of Mathematics. 2007. Vol. 129, num. 6, pags. 1689-1709. ISSN 0002-9327. [consulted: 6 of October of 2026]. Available at: https://hdl.handle.net/2445/197441

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