Conics in quintic del Pezzo varieties

2023/05/14 by Kiryong Chung, Chung, Kiryong, Sanghyeon Lee +1
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2305.08106

openalex publication_date 2023/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The smooth quintic del Pezzo variety Y is well-known to be obtained as a linear sections of the Grassmannian variety Gr(2,5) under the Plücker embedding into ℙ⁹. Through a local computation, we show the Hilbert scheme of conics in Y for dim Y ≥ 3 can be obtained from a certain Grassmannian bundle by a single blowing up/down transformation.

Related

• Local structure of the Hilbert scheme of conics in quintic del Pezzo varieties
• Quartic curves in the quintic del Pezzo threefold
• Variety of apolar schemes to powers of quadrics
• Hilbert property for double conic bundles and del Pezzo varieties
• Degenerations of Del Pezzo surfaces and the Gromov-Witten invariants of the Hilbert Scheme of conics