Tropical intersection theory [Elektronische Ressource] / Lars Allermann

Tropical intersection theoryLars AllermannVom Fachbereich Mathematikder Technischen Universit¨at Kaiserslauternzur Verleihung des akademischen GradesDoktor der Naturwissenschaften(Doctor rerum naturalium, Dr. rer. nat.)genehmigte Dissertation1. Gutachter: Prof. Dr. Andreas Gathmann2. Gutachter: Prof. Dr. Bernd SturmfelsVollzug der Promotion: 20.01.2010D 386ContentsPreface v1 Foundations of tropical intersection theory 11.1 Affine tropical cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Affine Cartier divisors and their associated Weil divisors . . . . . . . . 81.3 Push-forward of affine cycles and pull-back of Cartier divisors . . . . . 131.4 Abstract tropical cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.5 Cartier divisors and their associated Weil divisors . . . . . . . . . . . . 261.6 Push-forward of tropical cycles and pull-back of Cartier divisors . . . . 291.7 Rational equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32n1.8 Intersection of cycles inR . . . . . . . . . . . . . . . . . . . . . . . . . 34n1.9 Rational equivalence onR . . . . . . . . . . . . . . . . . . . . . . . . 392 Tropical cycles with real slopes and numerical equivalence 452.1 Tropical cycles with real slopes . . . . . . . . . . . . . . . . . . . . . . 452.2 Numerical equivalence on fans . . . . . . . . . . . . . . . . . . . . . . . 502.3 Chow groups via numerical equivalence . . . . . . . . . . . . . . . . . .