Geometry of the Kimura 3-parameter model

Local description of phylogenetic group-based models

Motivated by phylogenetics, our aim is to obtain a system of equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based models. For any finite abelian group $G$, we provide an explicit construction of $codim X$ phylogenetic invariants (polynomial equations) of degree at most $|G|$ that define the variety $X$ on a Zariski open set $U$. The set $U$ contains all biologically meaningful points when $G$ is the group of the Kimura 3-parameter model. In particular, our main result …

Improvement on Parameters of Algebraic-Geometry Codes from Hermitian Curves

Motivated by Xing's method [7], we show that there exist [n,k,d] linear Hermitian codes over F_{q^2} with k+d>=n-3 for all sufficiently large q. This improves the asymptotic bound of Algebraic-Geometry codes from Hermitian curves given in [9,10].

On the parameters of Algebraic Geometry codes related to Arf semigroups

In this paper we compute the order (or Feng-Rao) bound on the minimum distance of one-point algebraic geometry codes, when the Weierstrass semigroup at the point Q is an Arf semigroup. The results developed to that purpose also provide the dimension of the improved geometric Goppa codes related to those.

关于2阶完全交集参数空间的理化几何

On the birational geometry of the parameter space for codimension 2 complete intersections

本文研究了2阶完全交集参数空间\bar{H}的理化几何，证明了其MMP收缩的存在性，并在特定情况下完成了MMP，进而证明了点Hilbert方案中存在完整曲线。

线性化函数域的 Riemann–Roch 空间的基及其在广义代数几何码中的应用

Bases for Riemann--Roch spaces of linearized function fields with applications to generalized algebraic geometry codes

该研究通过给出线性化函数域 Riemann–Roch 空间的显式基，建立广义代数几何码最小距离下界，并据此构造参数良好的编码。

An algebraic geometry approach to nonlinear parametric optimization in control

We present a method for nonlinear parametric optimization based on algebraic geometry. The problem to be studied, which arises in optimal control, is to minimize a polynomial function with parameters subject to semialgebraic constraints. The method uses Groebner bases computation in conjunction with the eigenvalue method for solving systems of polynomial equations. In this way, certain companion matrices are constructed off-line. Then, given the parameter value, an on-line algorithm is used to efficiently obtain the optimizer of the original optimization problem in real time.