Decomposition into pairs-of-pants for complex algebraic hypersurfaces
| dc.creator | Mikhalkin, Grigory | |
| dc.date | 2002-05-01 | |
| dc.date | 2003-11-19 | |
| dc.date.accessioned | 2026-07-07T04:48:12Z | |
| dc.date.available | 2026-07-07T04:48:12Z | |
| dc.description | It is well-known that a Riemann surface can be decomposed into the so-called pairs-of-pants. Each pair-of-pants is diffeomorphic to a Riemann sphere minus 3 points. We show that a smooth complex projective hypersurface of arbitrary dimension admits a similar decomposition. The n-dimensional pair-of-pants is diffeomorphic to the complex projective n-space minus n+2 hyperplanes. Alternatively, these decompositions can be treated as certain fibrations on the hypersurfaces. We show that there exists a singular fibration on the hypersurface with an n-dimensional polyhedral complex as its base and a real n-torus as its fiber. The base accomodates the geometric genus of a hypersurface V. Its homotopy type is a wedge of h^{n,0}(V) spheres S^n. | |
| dc.description | 35 pages, 9 figures, final version to appear in Topology | |
| dc.identifier | https://arxiv.org/abs/math/0205011 | |
| dc.identifier | http://arxiv.org/abs/math/0205011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63955 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 14J70 | |
| dc.title | Decomposition into pairs-of-pants for complex algebraic hypersurfaces | |
| dc.type | text |