Intersection Theory on Compact Tropical Toric Varieties - and Compactifications of Tropical Parameter Spaces

We study toric varieties over the tropical semifield. We define tropical cycles inside these toric varieties and extend the stable intersection of tropical cycles in real n-space to these toric varieties. In particular, we show that every tropical cycle can be degenerated into a sum of torus-invariant cycles. This allows us to tropicalize algebraic cycles of toric varieties over an algebraically closed field with non-Archimedean valuation. We see that the tropicalization map is a homomorphism on cycles and an isomorphism on cycle classes. Furthermore, we can use projective toric varieties to compactify known tropical varieties and study their combinatorics. We do this for the tropical Grassmannian in the Plücker embedding and compactify the tropical parameter space of rational degree d curves in tropical projective space using Chow quotients of the tropical Grassmannian.

About the author

Dr. Henning Meyer ist wissenschaftlicher Mitarbeiter am Lehrstuhl von Prof. Dr. Thomas Gries der Universität-GH Paderborn.

Product details

• Authors: Henning Meyer
• Publisher: Südwestdeutscher Verlag für Hochschulschriften
• Languages: German
• Product format: Paperback / Softback
• Released: 02.09.2011
• EAN: 9783838127002
• ISBN: 978-3-8381-2700-2
• No. of pages: 100
• Dimensions: 150 mm x 220 mm x 6 mm
• Weight: 168 g
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Geometry