Mathematics – Algebraic Geometry
Scientific paper
2011-12-29
Mathematics
Algebraic Geometry
17 pages
Scientific paper
Let $S$ be a smooth minimal surface of general type with a (rational) pencil of hyperelliptic curves of minimal genus $g$. We prove that if $K_S^2<4\chi(\mathcal O_S)-6,$ then $g$ is bounded. The surface $S$ is determined by the branch locus of the covering $S\rightarrow S/i,$ where $i$ is the hyperelliptic involution of $S.$ For $K_S^2<3\chi(\mathcal O_S)-6,$ we show how to determine the possibilities for this branch curve. As an application, given $g>4$ and $K_S^2-3\chi(\mathcal O_S)<-6,$ we compute the maximum value for $\chi(\mathcal O_S).$ This list of possibilities is sharp.
Rito Carlos
Sanchez Maria Marti
No associations
LandOfFree
Hyperelliptic surfaces with $K^2 < 4χ- 6$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Hyperelliptic surfaces with $K^2 < 4χ- 6$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hyperelliptic surfaces with $K^2 < 4χ- 6$ will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-728673