Skeleta of affine curves and surfaces
dc.contributor.author | Thapa Magar, Surya | |
dc.date.accessioned | 2015-08-14T20:52:46Z | |
dc.date.available | 2015-08-14T20:52:46Z | |
dc.date.graduationmonth | August | en_US |
dc.date.issued | 2015-08-01 | en_US |
dc.date.published | 2015 | en_US |
dc.description.abstract | A smooth affine hypersurface of complex dimension n is homotopy equivalent to a real n-dimensional cell complex. We describe a recipe of constructing such cell complex for the hypersurfaces of dimension 1 and 2, i.e. for curves and surfaces. We call such cell complex a skeleton of the hypersurface. In tropical geometry, to each hypersurface, there is an associated hypersurface, called tropical hypersurface given by degenerating a family of complex amoebas. The tropical hypersurface has a structure of a polyhedral complex and it is a base of a torus fibration of the hypersurface constructed by Mikhalkin. We introduce on the edges of a tropical hypersurface an orientation given by the gradient flow of some piece-wise linear function. With the help of this orientation, we choose some sections and fibers of the fibration.These sections and fibers constitute a cell complex and we prove that this complex is the skeleton by using decomposition of the coemoeba of a classical pair-of-pants. We state and prove our main results for the case of curves and surfaces in Chapters 4 and 5. | en_US |
dc.description.advisor | Ilia Zharkov | en_US |
dc.description.degree | Doctor of Philosophy | en_US |
dc.description.department | Mathematics | en_US |
dc.description.level | Doctoral | en_US |
dc.identifier.uri | http://hdl.handle.net/2097/20395 | |
dc.publisher | Kansas State University | en |
dc.subject | Skeleton | en_US |
dc.subject.umi | Mathematics (0405) | en_US |
dc.title | Skeleta of affine curves and surfaces | en_US |
dc.type | Dissertation | en_US |