相关论文: Lifting divisors with imposed ramifications on a g…

We study a notion of tropical linear series on metric graphs that combines two essential properties of tropicalizations of linear series on algebraic curves: the Baker-Norine rank and the independence rank. Our main results relate the local…

We define ramified and split models of elliptic surfaces and study the relation between the two models. We focus on certain rational elliptic surfaces from these points of views and as an application, we give an observation on bitantgent…

Let $k$ be a field. Let $X/k$ be a stable curve whose geometric irreducible components are smooth rational curves. Taking Stein factorization of its normalization, we get a conic. We show the conic is non-split in certain cases. As an…

We establish a congruence formula between $p$-adic logarithms of Heegner points for two elliptic curves with the same mod $p$ Galois representation. As a first application, we use the congruence formula when $p=2$ to explicitly construct…

We prove an analogue of Clifford's inequality for tropical curves. Next we focus on the hyperelliptic case and we characterize divisors attaining equality. Finally we speculate whether inequality in tropical Clifford's Theorem does imply…

Let $K$ be a complete discrete valuation field whose residue field is perfect and of positive characteristic, let $X$ be a connected, proper scheme over $\mathcal{O}_K$, and let $U$ be the complement in $X$ of a divisor with simple normal…

We prove that a connected graph has linear rank-width 1 if and only if it is a distance-hereditary graph and its split decomposition tree is a path. An immediate consequence is that one can decide in linear time whether a graph has linear…

In this paper we study skeleta of residually tame coverings of a marked curve over a non-archimedean field. We first generalize a result by Liu and Lorenzini by proving a simultaneous semistable reduction theorem for residually tame…

Let $G$ be an acylic directed graph. For each vertex $g \in G$, we define an involution on the independent sets of $G$. We call these involutions flips, and use them to define a new partial order on independent sets of $G$. Trim lattices…

The aim of this chapter is to provide an adequate graph theoretic framework for the description of periodic bifurcations which have recently been discovered in descendant trees of finite p-groups. The graph theoretic concepts of rooted…

Connections between structural graph theory and finite model theory recently gained a lot of attention. In this setting, many interesting questions remain on the properties of dependent (NIP) hereditary classes of graphs, in particular…

Suppose $Y$ is a smooth variety equipped with a top form. We prove a simple theorem giving a sharp lower bound on the geometric genus of a family of subvarieties of $Y$, in terms of the dimension of this family. Two elementary applications…

Let $K$ be a complete discrete valuation field. Let $\mathcal{O}_K$ be its ring of integers. Let $k$ be its residue field which we assume to be algebraically closed of characteristic exponent $p\geq1$. Let $G/K$ be a semi-abelian variety.…

Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…

This paper gives a novel and compact proof that a metric graph consisting of a chain of loops of torsion order $0$ is Brill-Noether general (a theorem of Cools-Draisma-Payne-Robeva), and a finite or metric graph consisting of a chain of…

Let k be an algebraically closed field of characteristic 0. We prove that any division algebra over k(x,y) whose ramification locus lies on a quartic curve is cyclic.

In this paper we prove the algebraic-tropical correspondence for stable maps of rational curves with marked points to toric varieties such that the marked points are mapped to given orbits in the big torus and in the boundary divisor, the…

The classification of elliptic curves E over the rationals Q is studied according to their torsion subgroups E_{tors}(Q) of rational points. Explicit criteria for the classification are given when E_{tors}(Q) are cyclic groups with even…

We construct a connection and a curving on a bundle gerbe associated with lifting a structure group of a principal bundle to a central extension. The construction is based on certain structures on the bundle, i.e. connections and…

Given a Galois cover of curves X to Y with Galois group G which is totally ramified at a point x and unramified elsewhere, restriction to the punctured formal neighborhood of x induces a Galois extension of Laurent series rings…