Maps from K-trivial varieties and connectedness problems

Lazić, Vladimir; Peternell, Thomas

doi:10.5802/ahl.38

Cited by 2 publications

(4 citation statements)

References 31 publications

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“…Using a very nice result of Lazić and Peternell [20,Theorem 6.12] we can do slightly better in the smooth case.…”

Section: Question 02 Under Which Conditions a Genus-one Fibration Dmentioning

confidence: 93%

“…For smooth varieties we can do slightly better. The key point for this improvement is a very nice result for varieties covered by elliptic curves by Lazic and Peternell [20,Theorem 6.12]. For smooth varieties we can prove, using their result, the following corollary.…”

Section: Remark 44mentioning

confidence: 94%

“…Suppose by contradiction that X does not contain rational curves. We can apply [20,Theorem 6.12] and find an equidimensional fiber space X → W . This fibration is relatively minimal and we can proceed as in the proof of Theorem 0.4 and find an irregular quasi-étale cover of X .…”

Section: Remark 44mentioning

confidence: 99%

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Rational curves on genus-one fibrations

Anella

2020

manuscripta math.

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In this paper we look for necessary and sufficient conditions for a genus-one fibration to have rational curves. We show that a projective variety with log terminal singularities that admits a relatively minimal genus-one fibration $$X\rightarrow B$$ X → B does contain vertical rational curves if and only if it not isomorphic to a finite étale quotient of a product $$\tilde{B}\times E$$ B ~ × E over B. Many sufficient conditions for the existence of rational curves in a variety that admits a genus-one fibration are proved in this paper.

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“…Using a very nice result of Lazić and Peternell [20,Theorem 6.12] we can do slightly better in the smooth case.…”

Section: Question 02 Under Which Conditions a Genus-one Fibration Dmentioning

confidence: 93%

Section: Remark 44mentioning

confidence: 94%

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Rational curves on genus-one fibrations

Anella

2020

manuscripta math.

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“…In view of the arguments used by Lazić and Peternell [LP20], we might ask even more boldly for a relation between Pseff(P(Ω S )) and families of elliptic curves on S. Gounelas and Ottem [GO20] give a natural framework for these questions: the embedding P (Ω S ) ⊂ S [2] in the Hilbert square allows one to use results on the pseudoeffective cone of S [2] by Bayer and Macrì [BM14]. For example this approach allows one to recover the following classical result.…”

Section: Introduction 1motivationmentioning

confidence: 99%

The cotangent bundle of K3 surfaces of degree two

Fabrizio¹,

Höring²

2023

Épijournal De Géométrie Algébrique

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K3 surfaces have been studied from many points of view, but the positivity of the cotangent bundle is not well understood. In this paper we explore the surprisingly rich geometry of the projectivised cotangent bundle of a very general polarised K3 surface $S$ of degree two. In particular, we describe the geometry of a surface $D_S \subset \mathbb{P}(\Omega_S)$ that plays a similar role to the surface of bitangents for a quartic in $\mathbb{P}^3$.

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Maps from K-trivial varieties and connectedness problems

Cited by 2 publications

References 31 publications

Rational curves on genus-one fibrations

Rational curves on genus-one fibrations

The cotangent bundle of K3 surfaces of degree two

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