Rational connectivity and analytic contractibility
| Autor: | Morgan V. Brown, Tyler Foster |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Ring (mathematics) Applied Mathematics General Mathematics Laurent series Homotopy 010102 general mathematics 01 natural sciences Contractible space Morphism 0103 physical sciences ComputingMethodologies_DOCUMENTANDTEXTPROCESSING 010307 mathematical physics Birational invariant 0101 mathematics Algebraically closed field Projective variety Mathematics |
| Zdroj: | Journal für die reine und angewandte Mathematik (Crelles Journal). 2019:45-62 |
| ISSN: | 1435-5345 0075-4102 |
| DOI: | 10.1515/crelle-2016-0019 |
| Popis: | Let k {{k}} be an algebraically closed field of characteristic 0, and let f : X → Y {f:X\to Y} be a morphism of smooth projective varieties over the ring k ( ( t ) ) {k((t))} of formal Laurent series. We prove that if a general geometric fiber of f is rationally connected, then the induced map f an : X an → Y an {f^{\mathrm{an}}:X^{\mathrm{an}}\to Y^{\mathrm{an}}} between the Berkovich analytifications of X and Y is a homotopy equivalence. Two important consequences of this result are that the Berkovich analytification of any ℙ n {\mathbb{P}^{n}} -bundle over a smooth projective k ( ( t ) ) {k((t))} -variety is homotopy equivalent to the Berkovich analytification of the base, and that the Berkovich analytification of a rationally connected smooth projective variety over k ( ( t ) ) {k((t))} is contractible. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|