相关论文: Counting (tropical) curves via scattering.sage
This paper presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are…
We define tropical Psi-classes on the moduli space of rational tropical curves in R^2 and consider intersection products of Psi-classes and pull-backs of evaluations on this space. We show a certain WDVV equation which is sufficient to…
A bicyclic pair is a smooth surface equipped with a pair of smooth divisors intersecting in two reduced points. Resolutions of self-nodal curves constitute an important special case. We investigate the logarithmic Gromov-Witten theory of…
Using degeneration techniques, we prove the correspondence of tropical curve counts and log Gromov-Witten invariants with general incidence and psi-class conditions in toric varieties for genus zero curves and all non-superabundant…
We present two effective tools for computing the positive tropicalization of algebraic varieties. First, we outline conditions under which the initial ideal can be used to compute the positive tropicalization, offering a real analogue to…
In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study…
The objective of this paper is to lay out the algebraic theory of supertropical vector spaces and linear algebra, utilizing the key antisymmetric relation of ``ghost surpasses.''Special attention is paid to the various notions of ``base,''…
In this paper, we define two numbers. One comes from counting tropical curves with a stop and the other is the number of holomorphic discs in toric varieties with Lagrangian boundary condition. Both of these curves should satisfy some…
We give a tropical description of the counting of real log curves in toric degenerations of toric varieties. We treat the case of genus zero curves and all non-superabundant higher-genus situations. The proof relies on log deformation…
For certain tropical quartic curves the existing techniques could not predict the lifting behavior of their bitangents over the real numbers. We close this gap by using patchworking techniques. Further, this paper provides an analysis of…
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) Gromov-Witten invariants of projective spaces…
This paper is the first part in a series of three papers devoted to the study of enumerative invariants of abelian surfaces through the tropical approach. In this paper, we consider the enumeration of genus $g$ curves of fixed degree…
We give an overview of recently implemented polymake features for computations in tropical geometry. The main focus is on explicit examples rather than technical explanations. Our computations employ tropical hypersurfaces, moduli of…
We study log Calabi-Yau varieties obtained as a blow-up of a toric variety along hypersurfaces in its toric boundary. Mirrors to such varieties are constructed by Gross-Siebert from a canonical scattering diagram built by using punctured…
We present a direct and simple method for the computation of the total scattering matrix of an arbitrary finite noncompact connected quantum graph given its metric structure and local scattering data at each vertex. The method is inspired…
We describe an algorithm for computing certain characteristic numbers of surface scrolls using degenerations. As a corollary we obtain a method for computing the corresponding Gromov-Witten invariants of Grassmannians.
Given a curve defined over an algebraically closed field which is complete with respect to a nontrivial valuation, we study its tropical Jacobian. This is done by first tropicalizing the curve, and then computing the Jacobian of the…
We introduce tropical complexes, as an enrichment of the dual complex of a degeneration with additional data from non-transverse intersection numbers. We define cycles, divisors, and linear equivalence on tropical complexes, analogous both…
The theory of the topological vertex was originally proposed by Aganagic, Klemm, Mari\~no and Vafa as a means to calculate open Gromov-Witten invariants of toric Calabi-Yau threefolds. In this paper, we place the topological vertex within…
Block and G\"ottsche have defined a $q$-number refinement of counts of tropical curves in $\mathbb{R}^2$. Under the change of variables $q=e^{iu}$, we show that the result is a generating series of higher genus log Gromov-Witten invariants…