Resumen de Smooth tropical complete intersection curves of genus 3 in R3

Masayuki Sukenaga

• We develop a method for describing the tropical complete intersection of a tropical hypersurface and a tropical plane in R3. This involves a method for determining the topological type of the intersection of a tropical plane curve and R2≤0 by using a polyhedral complex. As an application, we study smooth tropical complete intersection curves of genus 3 in R3. In particular, we show that there are no smooth tropical complete intersection curves in R3 whose skeletons are the lollipop graph of genus 3. This gives a partial answer to a problem of Morrison in [6].