Algebraic proof of explicit formulas of basic relative invariants of homogeneous cones

一个基本相对不变量达到最大次数的齐性锥示例

An example of homogeneous cones whose basic relative invariant has maximal degree

该数学研究证明存在秩r的齐性锥，其基本相对不变量次数可达上界$2^{r-1}$，通过归纳构造带特定结构常数的齐性锥实现，并以秩3锥为例验证存在性的非平凡性。

Rational curves on homogeneous cones

Let G/Q be an homogeneous variety embedded in a projective space P thanks to an ample line bundle L. Take a projective space containing P and form the cone X over G/Q, we call this a cone over an homogeneous variety. Let $α$ a class of 1-cycle on X. In this article we describe the irreducible components of the scheme of morphisms of class $α$ from a rational curve to X. The situation depends on the line bundle L : if the projectivised tangent space to the vertex contains lines (i.e. if G/Q contains lines in P) then the irreducible components are described as in our paper math.AG/0407123 by the…

极小双曲多项式与齐次锥的秩

Minimal hyperbolic polynomials and ranks of homogeneous cones

本文围绕弦稀疏模式对应锥的对偶的极小双曲多项式计算展开，探究齐次锥秩与极小多项式的关联，否定了过往论文的一个问题，并给出非秩一生成（ROG）双曲性锥的齐次锥实例。

The cone conjecture for abelian varieties

We give a proof of the Morrison--Kawamata cone conjecture for abelian varieties. The proof is a straightforward deduction from well-known results on the real endomorphism algebra of an abelian variety and reduction theory for self-dual homogeneous convex cones.

Betti numbers for certain Cohen-Macaulay tangent cones

In this article, we compute Betti numbers for a Cohen-Macaulay tangent cone of a monomial curve in the affine $4$-space corresponding to a pseudo symmetric numerical semigroup. As a byproduct, we also show that for these semigroups, being of homogeneous type and homogeneous are equivalent properties.

齐性空间中的抛物线轨道集合、齐性动力学与超凯勒几何

Collections of parabolic orbits in homogeneous spaces, homogeneous dynamics and hyperkahler geometry

该研究针对满足$b_2(M)\u003e=5$的超凯勒流形，运用齐性空间遍历理论改进Morrison-Kawamata锥猜想相关结果，证明本原MBM类的Beauville-Bogomolov平方绝对值有仅依赖流形形变类的上界。