Geometry of syzygies via Poncelet varieties

2008/06/30 by Giovanna Ilardi, Ilardi, Giovanna, Paola Supino +3 · 1 citation
Mathematics · #Mathematics and Applications #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.0806.4881

Abstract

We consider the Grassmannian \mathbbGr(k,n) of (k+1)-dimensional linear subspaces of V_n=H⁰(¶¹,Ø_¶¹(n)). We define \frakX_k,r,d as the classifying space of the k-dimensional linear systems of degree n on ¶¹ whose basis realize a fixed number of polynomial relations of fixed degree, say a fixed number of syzygies of a certain degree. The first result of this paper is the computation of the dimension of \frakX_k,r,d. In the second part we make a link between \frakX_k,r,d and the Poncelet varieties. In particular, we prove that the existence of linear syzygies implies the existence of singularities on the Poncelet varieties.

Cited by

• On plane rational curves and the splitting of the tangent bundle

Related

• Restricting linear syzygies: algebra and geometry
• A structure theorem for syzygies of del Pezzo varieties
• Linear syzygies of projective space
• Syzygies using vector bundles
• Restricting linear syzygies: algebra and geometry