On Polarized K3 Surfaces of Genus 33

Karzhemanov, Ilya

doi:10.4153/cmb-2016-049-x

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2017

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“…In [Muk09], he also announced the case g = 17. The unirationality was recently shown for g = 14 and g = 33 in [Nue16] and [Kar16], respectively.…”

Section: Introductionmentioning

confidence: 71%

Moduli of lattice polarized K3 surfaces via relative canonical resolutions

Bopp¹

2017

Preprint

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For a smooth canonically embedded curve C of genus 9 together with a pencil |L| of degree 6, we study the relative canonical resolution of C ⊂ X ⊂ P 8 , where X is the scroll swept out by the pencil |L|. We show that the second syzygy bundle in this resolution of C ⊂ X is unbalanced. The proof reveals a new geometric connection between the universal Brill-Noether variety W 1 9,6 and a moduli space F h of lattice polarized K3 surfaces (for a certain rank 3 lattice h). As a by-product we prove the unirationality of F h and show that W 1 9,6 is birational to a projective bundle over a moduli space of lattice polarized K3 surfaces F h ′ for a certain rank 4 lattice h ′ which contains h as a sublattice.

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“…In [Muk09], he also announced the case g = 17. The unirationality was recently shown for g = 14 and g = 33 in [Nue16] and [Kar16], respectively.…”

Section: Introductionmentioning

confidence: 71%