Birational Finite Extensions of Mappings from a Smooth Variety

Marek Karaś. "Birational Finite Extensions of Mappings from a Smooth Variety." Bulletin of the Polish Academy of Sciences. Mathematics 57.2 (2009): 117-120. <http://eudml.org/doc/281135>.

@article{MarekKaraś2009,
abstract = {We present an example of finite mappings of algebraic varieties f:V → W, where V ⊂ kⁿ, $W ⊂ k^\{n+1\}$, and $F:kⁿ → k^\{n+1\}$ such that $F|_\{V\} = f$ and gdeg F = 1 < gdeg f (gdeg h means the number of points in the generic fiber of h). Thus, in some sense, the result of this note improves our result in J. Pure Appl. Algebra 148 (2000) where it was shown that this phenomenon can occur when V ⊂ kⁿ, $W ⊂ k^\{m\}$ with m ≥ n+2. In the case V,W ⊂ kⁿ a similar example does not exist.},
author = {Marek Karaś},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {finite mapping; birational mapping; geometric degree},
language = {eng},
number = {2},
pages = {117-120},
title = {Birational Finite Extensions of Mappings from a Smooth Variety},
url = {http://eudml.org/doc/281135},
volume = {57},
year = {2009},
}

TY - JOUR
AU - Marek Karaś
TI - Birational Finite Extensions of Mappings from a Smooth Variety
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2009
VL - 57
IS - 2
SP - 117
EP - 120
AB - We present an example of finite mappings of algebraic varieties f:V → W, where V ⊂ kⁿ, $W ⊂ k^{n+1}$, and $F:kⁿ → k^{n+1}$ such that $F|_{V} = f$ and gdeg F = 1 < gdeg f (gdeg h means the number of points in the generic fiber of h). Thus, in some sense, the result of this note improves our result in J. Pure Appl. Algebra 148 (2000) where it was shown that this phenomenon can occur when V ⊂ kⁿ, $W ⊂ k^{m}$ with m ≥ n+2. In the case V,W ⊂ kⁿ a similar example does not exist.
LA - eng
KW - finite mapping; birational mapping; geometric degree
UR - http://eudml.org/doc/281135
ER -