Related papers: Tropical Abel-Jacobi theory

We study two dimensional and three dimensional tropical subrepresentations of the regular representation $\mathbb{B}[G]$ of a finite group over the tropical booleans, utilizing the theory of group representations over a fixed idempotent…

We propose a generalization of tropical curves by dropping the rationality and integrality requirements while preserving the balancing condition. An interpretation of such curves as critical points of a certain quadratic functional allows…

We extend the usual projective Abel-Radon transform to the larger context of a smooth complete toric variety X. We define and study toric concavity attached to an algebraic splitting vector bundle on X and we prove a toric version of the…

Using equivariant obstruction theory we construct equivariant maps from certain classifying spaces to representation spheres for cyclic groups, product of elementary Abelian groups and dihedral groups. Restricting them to finite skeleta…

We look into a construction of principal abelian varieties attached to certain spin manifolds, due to Witten and Moore-Witten around 2000 and try to place it in a broader framework. This is related to Weil intermediate Jacobians but it also…

Tropical recurrent sequences are introduced satisfying a given vector (being a tropical counterpart of classical linear recurrent sequences). We consider the case when Newton polygon of the vector has a single (bounded) edge. In this case…

Let $X$ be a smooth cubic threefold and $J(X)$ be its intermediate Jacobian. We show that there exists a codimension 2 cycle $Z$ on $J(X)\times X$ with $Z_{t}$ homologically trivial for each $t\in J(X)$, such that the morphism $\phi_{Z}:…

We construct an Abel-Jacobi type map on the homologically trivial part of Lawson homology groups. It generalizes the Abel-Jacobi map constructed by Griffiths. By using a result of H. Clemens, we give some examples of smooth projective…

In this article, we study the infinitemisal invariant of the relative higher Abel Jacobi map of a smooth open morphism. We give a generalization of a theorem of Voisin to open varieties and higher Chow groups and as a corollary a non…

We propose a definition of tropical linear series that isolates some of the essential combinatorial properties of tropicalizations of not-necessarily-complete linear series on algebraic curves. The definition combines the Baker-Norine…

This paper gives a conjectural characterization of those elliptic curves over the field of complex numbers which "should" be covered by standard modular curves. The elliptic curves in question all have algebraic j-invariant, so they can be…

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…

We introduce the notion of tropical area of a tropical curve defined in an open subset of $\mathbb R^n$. We prove that the number of vertices of a tropical curve is bounded by the area of the curve. The approach is totally elementary yet…

This article applies the technical framework developed in previous work by the author to discrete admissible covers and their moduli spaces. More precisely, we construct a poic-space that parameterizes the discrete admissible covers after…

We construct classes in the motivic cohomology of certain 1-parameter families of Calabi-Yau hypersurfaces in toric Fano n-folds, with applications to local mirror symmetry (growth of genus 0 instanton numbers) and inhomogeneous…

To a tropical $p$-cycle $V_{\mathbb{T}}$ in $\mathbb{R}^n$, we naturally associate a normal closed and $(p,p)$-dimensional current on $(\mathbb{C}^*)^n$ denoted by $\mathscr{T}_n^p(V_{\mathbb{T}})$. Such a "tropical current"…

We use piecewise polynomials to define tropical cocycles generalising the well-known notion of tropical Cartier divisors to higher codimensions. Groups of cocycles are tropical analogues of Chow cohomology groups. We also introduce an…

Let C be a complex curve of genus g, let J(C) be its Jacobian and let R(C) be its tautological ring, that is, the group of algebraic cycles modulo algebraic equivalence. We study the algebraic structure of R(C). In particular, we give a…

On \'etudie les cycles alg\'ebriques de codimension 3 sur les hypersurfaces cubiques lisses de dimension 5. Pour une telle hypersurface, on d\'emontre d'une part que son groupe de Griffiths des cycles de codimension 3 est trivial et d'autre…

We present a new technique to study Jacobian variety decompositions using subgroups of the automorphism group of the curve and the corresponding intermediate covers. In particular, this new method allows us to produce many new examples of…