Support provided by NSF RTG grant DMS-1246844.

Notes and Resources

 

• DRAFT VERSION "An introduction to volume functions for algebraic cycles" (written for the workshop)

 

• John Lesieutre (UIC) - Introduction
  • HANDWRITTEN NOTES
  • 3264 & All That: Intersection Theory in Algebraic Geometry (Eisenbud and Harris) .
    • Chapter 1 & Appendix C3
  • Positivity in Algebraic Geometry I (Lazarsfeld)
    • Chapter 1
  • Quick guide to positive cones of numerical classes (Fulger and Lehmann)

 

• Mihai Fulger (Princeton University) - The structure of pseudoeffective cones
  • HANDWRITTEN NOTES (and problem sheet from the lecture at the end)
  • Positive cones of dual cycle classes (Fulger and Lehmann)
  • Zariski decompositions of numerical cycle classes (Fulger and Lehmann)
  • Morphisms and faces of pseudo-effective cone  (Fulger and Lehmann)
  • Pseudoeffective classes and pushforwards (Debarre, Jiang, and Voisin)

 

• Brian Lehmann (Boston College) - Asymptotic point counts
  • HANDWRITTEN NOTES (and problem sheet)
  • Asymptotic invariants of line bundles (Ein, Lazarsfeld, Mustata, Nakamaye, Popa)
  •  Volume-type functions for numerical cycle classes (Lehmann)
  • Zariski decompositions of numerical cycle classes (Fulger and Lehmann)
  • Characterizing volume via cone duality (Xiao)
  • Convexity and Zariski decomposition structure (Lehmann and Xiao)
  • Positivity functions for curves on algebraic varieties (Lehmann and Xiao)

 

• John Ottem (Cambridge/Oslo) - Ample normal bundles and pseudoeffective cones
  • HANDWRITTEN NOTES (and problem sheet)
  • Positivity in Algebraic Geometry II (Lazarsfeld)
    • Chapter 6
  • Ample subvarieties and q-ample divisors (Ottem)
  • On subvarieties with ample normal bundle (Ottem)
  • Pseudoeffective and nef classes on abelian varieties (Debarre, Ein, Lazarsfeld, Voisin)