# Tropical intersection products on smooth varieties

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 1, page 107-126
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topAllermann, 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 -