Lines, conics, and all that

Ciliberto, Ciro; Zaidenberg, Mikhail

doi:10.48550/arxiv.1910.11423

Cited by 4 publications

(4 citation statements)

References 191 publications

(250 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The study of Hilbert scheme of low degree rational curves is a classical topic in enumerative geometry. An excellent survey is [CZ19]. A comprehensive treatment on fano variety of lines and conics on Fano threefolds is given in [KPS].…”

mentioning

confidence: 99%

Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture

Zhang

2020

Preprint

View full text Add to dashboard Cite

We study the Hilbert scheme H of twisted cubics on a special smooth Gushel-Mukai threefolds X10. We show that it is a smooth irreducible projective threefold if X10 is general among special Gushel-Mukai threefolds, while it is singular and irreducible if X10 is not general. We construct an irreducible component of a moduli space of Bridgeland stable objects in the Kuznetsov component of X10 as a divisorial contraction of H. We also identify the minimal model of Fano surface C(X ′ 10 ) of conics on a smooth ordinary Gushel-Mukai threefold with an irreducible component of a moduli space of Bridgeland stable objects in the Kuznetsov component of X ′ 10 . As a result, we show that the Kuznetsov's Fano threefold conjecture is not true.

show abstract

mentioning

confidence: 99%

Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture

Zhang

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…where C is the conic corresponding to s. It is well-known that every conic C on X can be realized as the zero scheme of a global section R ∨ (see [4,Theorem 5.6] and its reference). Since H ≥2 (E) = 0 by [18, Lemma 3.1], it is enough to show that H ≥2 (I C (1) ⊗ E) = 0 for a general conic C. This vanishing holds since it was shown by [26,Theorem 4.24] that E| C ≃ O ⊕2 P 1 for a general conic C. We complete the proof.…”

Section: Therefore If We Can Computementioning

confidence: 99%

Rank two weak Fano bundles on del Pezzo threefolds of Picard rank one

Fukuoka¹,

Hara²,

Ishikawa³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…These date back to at least two centuries ago represented by a result of 27 lines on a cubic surface. See, e.g., a survey paper [CZ20] and references therein for a history and results on low degree rational curves.…”

Section: Introductionmentioning

confidence: 99%