On a minimal factorization conjecture
Let be a proper holomorphic map from a connected complex surface S onto the open unit disk D⊂C, with 0∈D as its unique singular value, and having fiber genus g>0 -- Assume that in case g⩾2, admits a deformation whose singular fibers are all of simple Lefschetz type -- It has been conjectured that...
- Autores:
-
Cadavid, Carlos A.
Vélez, Juan D.
- Tipo de recurso:
- Fecha de publicación:
- 2007
- Institución:
- Universidad EAFIT
- Repositorio:
- Repositorio EAFIT
- Idioma:
- eng
- OAI Identifier:
- oai:repository.eafit.edu.co:10784/9780
- Acceso en línea:
- http://hdl.handle.net/10784/9780
- Palabra clave:
- SUPERFICIES DE RIEMANN
TOPOLOGÍA ALGEBRÁICA
GEOMETRÍA DIFERENCIAL
ANÁLISIS MATEMÁTICO
ISOMORFISMO (MATEMÁTICAS)
Riemann surfaces
Algebraic topology
Geometry, differential
Mathematical analysis
Isomorphisms (Mathematics)
Riemann surfaces
Algebraic topology
Geometry
differential
Mathematical analysis
Isomorphisms (Mathematics)
Fibraciones elípticas
Monodromía
- Rights
- License
- Acceso abierto
| Summary: | Let be a proper holomorphic map from a connected complex surface S onto the open unit disk D⊂C, with 0∈D as its unique singular value, and having fiber genus g>0 -- Assume that in case g⩾2, admits a deformation whose singular fibers are all of simple Lefschetz type -- It has been conjectured that the factorization of the monodromy f∈M around ϕ (0) in terms of righ-thanded Dehn twists induced by the monodromy of has the least number of factors among all possible factorizations of f as a product of righthanded Dehn twists in the mapping class group (see [M. Ishizaka, One parameter families of Riemann surfaces and presentations of elements of mapping class group by Dehn twists, J. Math. Soc. Japan 58 (2) (2006) 585–594]) -- In this article, the validity of this conjecture is established for g=1 |
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