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• Tags:
  • #AG/complex
• Refs:
  • Huybrechts lectures: https://www.math.uni-bonn.de/people/huybrech/K3Global.pdf#page=1 #resources/notes/lectures
  • Beauville, rational curves on K3s https://arxiv.org/pdf/alg-geom/9701019.pdf#page=1 #resources/papers
  • More lecture notes: http://web.math.ucsb.edu/~drm/manuscripts/cortona.pdf#page=1 #projects/lecture-notes
  • Books:
    • W. Barth, K. Hulek, C. Peters, and A. Van de Ven. Compact complex surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, Berlin, 2004. #resources/books
    • A. Beauville et al. Géométrie des surfaces K3: modules et périodes http://www.numdam.org/item/AST_1985__126__1_0.pdf#page=1 #resources/papers
    • Dynamics on K3s: https://math.uchicago.edu/~sfilip/public_files/lectures_k3_dynamics.pdf#page=13&zoom=auto,-200,744
• Links:
  • Calabi-Yau
  • MMP
  • lattice
  • Hodge F-crystal

K3 Surfaces

Definitions

• Defining condition: trivial canonical bundle
• Special case (\(\dim_{\mathbf{C}}= 2\)) of Calabi-Yau manifolds

Relation to formal groups:

To compute these Hodge numbers, see https://d-nb.info/1196803269/34#page=14&zoom=160,-97,766

See Hodge structure

Examples

Taubes

Misc

Examples

The Kummer surface:

The Fermat quartic:

Pencils

Neron-Severi

Weyl group

# Kahler cone

Cohomology

Picard

#open/problems

Neron-Severi

Using crystalline cohomology:

Polarization

The DM Stack

Deformations:

Using periods

See level structure

Torelli map:

As a complex manifold

Stability

Automorphic forms

Heights

See F-crystal.

Lifts

Crystalline cohomology