GIT stability of linear systems of skew-symmetric forms

Abstract: Given a 6 dimensional vector space $W$, we consider $\mathbb{P}(\mathbb{C}^{n+1}\otimes \bigwedge ^2 W^*)$, the projective space parameterizing n-dimensional linear systems of skew-symmetric forms on $W$. Since the group $SL(W)$ acts on $\mathbb{P}(\mathbb{C}^{n+1}\otimes \bigwedge ^2 W^*)$, Geometric Invariant Theory (GIT) provides a notion of (semi)stability. In this talk I will introduce a criterion to detect the (semi)stability of linear systems of skew-symmetric forms and I will then present how this criterion allows to obtain a complete classification of all stable linear systems having generic rank equal to 4.

algebraic geometry

Audience: researchers in the topic

Comments: Access the Zoom link zoom.us/j/92887438541?pwd=Q3BHRU9CcFBicTJ1eXhacVpLOERKUT09

---

Brazilian algebraic geometry seminar

Series comments: Subscribe the seminar mailing list, please send and email to brag-seminar-request@lists.ime.unicamp.br with "subscribe" in the subject line.

Previous talks available at the YouTube channel "Brazilian Algebraic Geometry" www.youtube.com/channel/UCM-pcdNdpWxQFgOg-illE2w

---