Nef cycles on some hyperkahler fourfolds
John Christian Ottem
TL;DR
This paper investigates the geometric properties of certain cycles on hyperkähler fourfolds, revealing new nef cycles that are not pseudoeffective, through analysis of cones of surfaces on related varieties.
Contribution
It introduces new examples of nef cycles on hyperkähler fourfolds that are not pseudoeffective, expanding understanding of their geometric structure.
Findings
Discovery of nef cycles that are not pseudoeffective
Analysis of cones of surfaces on cubic fourfolds and K3 surface Hilbert schemes
New insights into the geometry of hyperkähler fourfolds
Abstract
We study the cones of surfaces on varieties of lines on cubic fourfolds and Hilbert schemes of points on K3 surfaces. From this we obtain new examples of nef cycles which fail to be pseudoeffective.
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