101 citations · 102 across the 3 of their papers we have counts for
6 papers
Amoebas of algebraic varieties and tropical geometry
Grigory Mikhalkin
This survey consists of two parts. Part 1 is devoted to amoebas. These are images of algebraic subvarieties in the complex torus under the logarithmic moment map. The amoebas have…
Enumerative tropical algebraic geometry in R2
Grigory Mikhalkin
The paper establishes a formula for enumeration of curves of arbitrary genus in toric surfaces. It turns out that such curves can be counted by means of certain lattice paths in th…
Counting curves via lattice paths in polygons
Grigory Mikhalkin
This note presents a formula for the enumerative invariants of arbitrary genus in toric surfaces. The formula computes the number of curves of a given genus through a collection of…
Decomposition into pairs-of-pants for complex algebraic hypersurfaces
Grigory Mikhalkin
It is well-known that a Riemann surface can be decomposed into the so-called pairs-of-pants. Each pair-of-pants is diffeomorphic to a Riemann sphere minus 3 points. We show that a…
Amoebas of algebraic varieties
Grigory Mikhalkin
The amoebas associated to algebraic varieties are certain concave regions in the Euclidean space whose shape reminds biological amoebas. This term was formally introduced to Mathem…
Amoebas of maximal area
Grigory Mikhalkin, Hans Rullgard
To any algebraic curve A in a complex 2-torus $(\C^*)^2$ one may associate a closed infinite region in a real plane called the amoeba of A. The amoebas of different curves of the s…