Tropical intersection products on smooth varieties

Allermann, Lars. "Tropical intersection products on smooth varieties." Journal of the European Mathematical Society 014.1 (2012): 107-126. <http://eudml.org/doc/277504>.

@article{Allermann2012,
abstract = {We define an intersection product of tropical cycles on tropical linear spaces $L^n_k$, i.e. on tropical fans of the type max$\lbrace 0,x_1,\ldots , x_n\rbrace ^\{n-k\}\cdot \mathbb \{R\}^n$. Afterwards we use this result to obtain an intersection product of cycles on every smooth tropical variety, i.e. on every tropical variety that arises from gluing such tropical linear spaces. In contrast to classical algebraic geometry these products always yield well-defined cycles, not cycle classes only. Using these intersection products we are able to define the pull-back of a tropical cycle along a morphism between smooth tropical varieties.},
author = {Allermann, Lars},
journal = {Journal of the European Mathematical Society},
keywords = {algebraic geometry; tropical geometry; intersection theory; linear space; fan; matroid; tropical geometry; intersection theory; linear space; fan; matroid},
language = {eng},
number = {1},
pages = {107-126},
publisher = {European Mathematical Society Publishing House},
title = {Tropical intersection products on smooth varieties},
url = {http://eudml.org/doc/277504},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Allermann, Lars
TI - Tropical intersection products on smooth varieties
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 1
SP - 107
EP - 126
AB - We define an intersection product of tropical cycles on tropical linear spaces $L^n_k$, i.e. on tropical fans of the type max$\lbrace 0,x_1,\ldots , x_n\rbrace ^{n-k}\cdot \mathbb {R}^n$. Afterwards we use this result to obtain an intersection product of cycles on every smooth tropical variety, i.e. on every tropical variety that arises from gluing such tropical linear spaces. In contrast to classical algebraic geometry these products always yield well-defined cycles, not cycle classes only. Using these intersection products we are able to define the pull-back of a tropical cycle along a morphism between smooth tropical varieties.
LA - eng
KW - algebraic geometry; tropical geometry; intersection theory; linear space; fan; matroid; tropical geometry; intersection theory; linear space; fan; matroid
UR - http://eudml.org/doc/277504
ER -