8 citations · 25 across the 12 of their papers we have counts for
12 papers
Riemannian metrics with prescribed volume and finite parts of Dirichlet spectrum
Xiang He, Zuoqin Wang
In this paper we study the problem of prescribing Dirichlet eigenvalues on an arbitrary compact manifold of dimension with a non-empty smooth boundary . W…
Prescription of finite Dirichlet eigenvalues and area on surface with boundary
Xiang He
In the present paper, we consider Dirichlet Laplacian on compact surface. We show that for a fixed surface with boundary , a finite increasing sequence of real numbers $0<a_1<a_…
Positivity of tropical multidegrees
Xiang He
We define the multidegrees of a tropical variety. We prove that the positivity of a multidegree of a certain tropical variety is governed by the dimensions of the images of the tro…
Degenerations of Grassmannians via lattice configurations II
Xiang He, Naizhen Zhang
This paper is a continuation of our study of degenerations of Grassmannians in our last paper, called linked Grassmannians, constructed using convex lattice configurations in Bruha…
Degeneration of curves on some polarized toric surfaces
Karl Christ, Xiang He, Ilya Tyomkin
We address the following question: Given a polarized toric surface (S,L), and a general integral curve C of geometric genus g in the linear system |L|, do there exist degenerations…
On the Severi problem in arbitrary characteristic
Karl Christ, Xiang He, Ilya Tyomkin
In this paper, we show that Severi varieties parameterizing irreducible reduced planar curves of a given degree and geometric genus are either empty or irreducible in any character…
Degenerations of Grassmannians via lattice configurations
Xiang He, Naizhen Zhang
We study degenerations of Grassmannians constructed using convex lattice configurations in Bruhat-Tits buildings. Using techniques from quiver representations, we analyze their spe…
Secant planes of a general curve via degenerations
Ethan Cotterill, Xiang He, Naizhen Zhang
We study linear series on a general curve of genus g, whose images are exceptional with respect to their secant planes. Each such exceptional secant plane is algebraically encoded…
Brill-Noether Generality of Binary Curves
Xiang He
We show that the space of linear series of certain multi-degree (including the balanced ones) and rank on a general binary curve has the expected dimension if nonempty. This ge…
Lifting divisors with imposed ramifications on a generic chain of loops
Xiang He
Proves that if a curve has totally split reduction and the corresponding skeleton (as a metric graph) is a chain of loops with generic edge lengths, then every divisor on the graph…
Smoothing of limit linear series on curves and metrized complexes of pseudocompact type
Xiang He
We investigate the connection between Osserman limit series (on curves of pseudocompact type) and Amini-Baker limit linear series (on metrized complexes with corresponding underlyi…
A Generalization of Lifting Non-proper Tropical Intersections
Xiang He
Let X and X' be closed subschemes of an algebraic torus T over a non-archimedean field. We prove the rational equivalence as tropical cycles, in the sense of Henning Meyer's gradua…