Year: 2026
Type: preprint
Abstract: Let $X\subset\mathbb P^N$ be a smooth complete intersection of two quadrics. We find formulas in the Grothendieck ring of varieties for the class of $X$ and for the class of its Fano scheme of lines, thereby proving the first two cases of a conjecture of Belmans et al. We also find a formula for the class of the relative Fano schemes of linear subspaces (of any dimension) in the fibers of quadric fibrations over curves, under a simple degeneration assumption. As consequences, we compute the rational Chow motive of the relative Fano scheme, and we provide evidence for a conjecture of Shah on a residual category in a semiorthogonal decomposition of the relative Fano scheme of lines.
Source: arXiv (Cornell University)
Authors: Ji, Lena, Suzuki, Fumiaki
Institution: University of Illinois Urbana-Champaign
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214998102