Equations for $\bar M_{0,n}$

Generalizations of Strassen's equations for secant varieties of Segre varieties

We define many new examples of modules of equations for secant varieties of Segre varieties that generalize Strassen's commutation equations. Our modules of equations are obtained by constructing subspaces of matrices from tensors that satisfy various commutation properties.

Equations for the third secant variety of the Segre product of n projective spaces

We determine set theoretic defining equations for the third secant variety of the Segre product of $n$ projective spaces, and from the proof of the main statement we derive an upper bound for the degrees of these equations.

Secant varieties of Segre-Veronese varieties P^m x P^n embedded by O(1,2)

Let $X_{m,n}$ be the Segre-Veronese variety $\mathbb{P}^m \times \mathbb{P}^n$ embedded by the morphism given by $\mathcal{O}(1,2)$. In this paper, we provide two functions $\underline{s}(m,n)\le \bar{s}(m,n)$ such that the $s^{\mathrm{th}}$ secant variety of $X_{m,n}$ has the expected dimension if $s \leq \underline{s}(m,n)$ or $ \bar{s}(m,n) \leq s$. We also present a conjecturally complete list of defective secant varieties of such Segre-Veronese varieties.

Equations for the fifth secant variety of Segre products of projective spaces

We describe a computational proof that the fifth secant variety of the Segre product of five copies of the projective line is a codimension 2 complete intersection of equations of degree 6 and 16. Our computations rely on pseudo-randomness, and numerical accuracy, so parts of our proof are only valid "with high probability".

Segre 簇的切触簇的集合论定义方程

Set-theoretic defining equations of the tangential variety of the Segre variety

本文证明了 Landsberg--Weyman 猜想的集合论版本，通过引入排他秩概念，将 Segre 簇的切触簇表示为排他秩不超过一的对称矩阵的主子式簇，从而给出其定义方程。

Segre-Grassmann 超曲面的计算与方程

Computations and Equations for Segre-Grassmann hypersurfaces

本文解答了Abo-Wan关于Segre-Grassmann超曲面的问题，证实无限族超曲面由已知行列式方程极小定义，并提供非数值证明。