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Author: Johannes Rau Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG ISBN: 9783838114286 Category : Languages : en Pages : 200
Book Description
In this publication a tropical intersection theory is established with analogue notions and tools as its algebro-geometric counterpart. The developed theory, interesting as a subfield of convex geometry on its own, shows many relations to the intersection theory of toric varieties and other fields. In the second chapter, tropical intersection theory is used to define and study tropical gravitational descendants (i.e. Gromov-Witten invariants with incidence and "Psi-class" factors). It turns out that many concepts of the classical Gromov-Witten theory such as the WDVV equations can be carried over to the tropical world.
Author: Johannes Rau Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG ISBN: 9783838114286 Category : Languages : en Pages : 200
Book Description
In this publication a tropical intersection theory is established with analogue notions and tools as its algebro-geometric counterpart. The developed theory, interesting as a subfield of convex geometry on its own, shows many relations to the intersection theory of toric varieties and other fields. In the second chapter, tropical intersection theory is used to define and study tropical gravitational descendants (i.e. Gromov-Witten invariants with incidence and "Psi-class" factors). It turns out that many concepts of the classical Gromov-Witten theory such as the WDVV equations can be carried over to the tropical world.
Author: Erwan Brugalle Publisher: American Mathematical Soc. ISBN: 0821891464 Category : Mathematics Languages : en Pages : 363
Book Description
This volume contains the proceedings of the CIEM workshop on Tropical Geometry, held December 12-16, 2011, at the International Centre for Mathematical Meetings (CIEM), Castro Urdiales, Spain. Tropical geometry is a new and rapidly developing field of mat
Author: Henning Meyer Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG ISBN: 9783838127002 Category : Tropical geometry Languages : de Pages : 100
Book Description
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 Plucker embedding and compactify the tropical parameter space of rational degree d curves in tropical projective space using Chow quotients of the tropical Grassmannian."
Author: Johannes Rau
Author: Johannes Rau
Author: Erwan Brugalle
Author: Lars Allermann
Author: Kristin Shaw
Author: Simon Hampe
Author: 
Author: Zhi Jin
Author: Henning Meyer
Author: Henning Meyer
Author: Matthias Herold