Morse theory and Euler characteristic of sections of spherical varieties
| dc.creator | Kaveh, Kiumars | |
| dc.date | 2001-12-06 | |
| dc.date.accessioned | 2026-07-07T04:45:04Z | |
| dc.date.available | 2026-07-07T04:45:04Z | |
| dc.description | A theorem due to D. Bernstein states that Euler characteristic of a hypersurface defined by a polynomial f in (C\{0})^n is equal (upto a sign) to n! times volume of the Newton polyhedron of f. This result is related to algebaric torus actions and toric varieties. In this thesis, I prove that one can generalize the above result to actions of reductive groups with spherical orbits. That is, if a reductive group acts linearly on a vector space such that generic orbits are spherical, one can compute the Euler characteristic of generic hyperplane sections of a generic orbit in terms of combinatorial data. Our main tool is Morse theory. We begin with developing a variant of classical Morse theory for algebraic submanifolds of R^n and linear functionals. This will become related to stratification theory of Thom and Whitney as well as Palais-Smale generalized Morse theory. | |
| dc.description | 69 pages | |
| dc.identifier | https://arxiv.org/abs/math/0112064 | |
| dc.identifier | http://arxiv.org/abs/math/0112064 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62836 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Morse theory and Euler characteristic of sections of spherical varieties | |
| dc.type | text |