# Secant Varieties Working Group

### Secant Varieties Working Group 2018/2019

(follow up to Secant Varieties Working Group of Varieties: Arithmetic and Transformations)

 meetings take place on: Wednesdays 11:30-13:00, room 403 in the winter semester: 9.01.2019, 16.01.2019, 23.01.2019, 30.01.2019, 6.02.2019, 13.02.2019, 20.02.2019, 27.02.2019, 6.03.2019, 13.03.2019, 20.03.2019 (in the room 408) 27.03.2019 10.04.2019 (in the room 321) Research problems we try to address: Find equations of secant varieties that do not vanish on cactus varieties. For a fixed tensor $T \in \mathbb{P}(\mathbb{C}^m \otimes \mathbb{C}^m \otimes \mathbb{C}^m)$ find criteria for $T$ to have border rank equal to $m$. High rank loci. For $X \in \mathbb{P}(V )$ let $W_r(X)$ be the closure of tensors in $\mathbb{P}(V)$ which have rank equal to $r$. Is there an equality between $W_k$ and $W_{k+1} + X$  for $k,  where $Y+Z$ denotes the join of $Y$ and $Z$? We are open to discuss any issues related to secant varieties, cactus varieties, tensor rank, Waring rank, and their border/cactus analogues, identifiability, apolarity, Hilbert schemes of points etc.

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