Rational curves on lattice-polarised K3 surfaces

Xi Chen; Frank Gounelas; Christian Liedtke

doi:10.14231/AG-2022-013

Rational curves on lattice-polarised K3 surfaces

Xi Chen
, Frank Gounelas
, Christian Liedtke

Chair of Algebraic Geometry

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Fix a K3 lattice Λ of rank 2 and a big and nef divisor L∈Λthat is suitably positive.We prove that the generic Λ-polarised K3 surface has an integral nodal rational curve in the linear system jLj, in particular strengthening previous work of the first-named author.

Original language	English
Pages (from-to)	443-475
Number of pages	33
Journal	Algebraic Geometry
Volume	9
Issue number	4
DOIs	https://doi.org/10.14231/AG-2022-013
State	Published - Jul 2022

Keywords

Degenerations of curves and surfaces.
K3 surface
Lattice polarisation
Rational curve

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10.14231/AG-2022-013

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abstract = "Fix a K3 lattice Λ of rank 2 and a big and nef divisor L∈Λthat is suitably positive.We prove that the generic Λ-polarised K3 surface has an integral nodal rational curve in the linear system jLj, in particular strengthening previous work of the first-named author.",

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author = "Xi Chen and Frank Gounelas and Christian Liedtke",

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AU - Liedtke, Christian

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PY - 2022/7

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N2 - Fix a K3 lattice Λ of rank 2 and a big and nef divisor L∈Λthat is suitably positive.We prove that the generic Λ-polarised K3 surface has an integral nodal rational curve in the linear system jLj, in particular strengthening previous work of the first-named author.

AB - Fix a K3 lattice Λ of rank 2 and a big and nef divisor L∈Λthat is suitably positive.We prove that the generic Λ-polarised K3 surface has an integral nodal rational curve in the linear system jLj, in particular strengthening previous work of the first-named author.

KW - Degenerations of curves and surfaces.

KW - K3 surface

KW - Lattice polarisation

KW - Rational curve

UR - https://www.scopus.com/pages/publications/85133318870

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DO - 10.14231/AG-2022-013

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JO - Algebraic Geometry

JF - Algebraic Geometry

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ER -

Rational curves on lattice-polarised K3 surfaces

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Keywords

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