• Tags
  • #todo/untagged
• Refs:
  • https://mathweb.ucsd.edu/~jmckerna/Teaching/14-15/Spring/207A/ #resources/full-courses
  • Introduction to MMP by Kawamata et al: https://projecteuclid.org/ebook/download?urlId=10.2969/aspm/01010283&isFullBook=false#page=1 #resources/notes
  • 2021 Course notes: https://www.math.columbia.edu/~plei/docs/MMP.pdf#page=2 #resources/course-notes
  •  Positivity in Algebraic Geometry I & II, by Lazarsfeld
• Links:
  • Chevalley-Eilenberg complex
  • Quillen minimal model program
  • nef divisor
  • Gorenstein

MMP

Blowups aren’t usually minimal models:

So restrict attention to minimal surfaces: those that are not the blowup of any smooth surface.

See:

• abelian surface, Jacobian
• K3 surface, canonical divisor
• Enriques surface
• bielliptic surface
• elliptic surface

Birational minimal model program

See flips

Results

The algorithm

Status