Smooth tropical complete intersection curves of genus 3 in \mathbb {R}^3
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Sukenaga, Masayuki [1]
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[1] Hiroshima University
Hiroshima University
Naka-ku, Japón
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- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 3, 2023, págs. 753-793
- Idioma: inglés
- DOI: 10.1007/s13348-022-00372-7
- Texto completo no disponible (Saber más ...)
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Resumen
We develop a method for describing the tropical complete intersection of a tropical hypersurface and a tropical plane in \mathbb {R}^3. This involves a method for determining the topological type of the intersection of a tropical plane curve and \mathbb {R}_{\le 0}^2 by using a polyhedral complex. As an application, we study smooth tropical complete intersection curves of genus 3 in \mathbb {R}^3. In particular, we show that there are no smooth tropical complete intersection curves in \mathbb {R}^3 whose skeletons are the lollipop graph of genus 3. This gives a partial answer to a problem of Morrison in [6].
