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Enumerative tropical algebraic geometry
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 the Newton polygon.Expand
Enumerative tropical algebraic geometry in R^2
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 the Newton polygon.Expand
Tropical geometry and its applications
From a formal perspective tropical geometry can be viewed as a branch of geometry manipulating with certain piecewise-linear objects that take over the role of classical algebraic varieties. ThisExpand
Tropical curves, their Jacobians and Theta functions
We study Jacobian varieties for tropical curves. These are real tori equipped with integral affine structure and symmetric bilinear form. We define tropical counterpart of the theta function andExpand
ENUMERATIVE TROPICAL ALGEBRAIC GEOMETRY IN R
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 the Newton polygon.Expand
Real algebraic curves, the moment map and amoebas
In this paper we prove the topological uniqueness of maximal arrangements of a real plane algebraic curve with respect to three lines. More generally, we prove the topological uniqueness of aExpand
Decomposition into pairs-of-pants for complex algebraic hypersurfaces
Abstract 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 smoothExpand
Labeled floor diagrams for plane curves
Floor diagrams are a class of weighted oriented graphs introduced by E. Brugalle and the second author. Tropical geometry arguments lead to combinatorial descriptions of (ordinary and relative)Expand
Enumeration of curves via floor diagrams
In this note we compute some enumerative invariants of real and complex projective spaces by means of some enriched graphs called floor diagrams.
Amoebas of Algebraic Varieties and Tropical Geometry
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 essentiallyExpand
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