Winter Semester 2014/2015
Meet Tuesdays at 10:45 in the seminar room 1.411 on our floor (Haus 1 floor 4 room 11). Starting week 3 on the 28th of October.
Here are the final handwritten notes from the course.
Last updated: 29/1/2015
Talk 1 (Frank 28/10/2014)
definitions
Mukai flop etc
deformation theory
Beauville-Bogomolov form
Talk 2 (Frank 4/11/2014)
Beauville-Bogomolov form
local Torelli
Fujiki's Lefschetz theorems and cohomology results
Talk 3 (Niels 11/11/2014)
birationally equivalent implies deformation equivalent
non-separability of points implies birational
examples of the above and why Verbitsky's global Torelli is stated as it is
Talk 4 (Mike 18/11/2014)
Kahler cone
Projectivity from section 9 in Huybrecht's Habilitation.
Talk 5 (Mike 25/11/2014)
More on projectivity
Talk 6 (Michael 9/12/2014)
Even more on projectivity
Talk 7 (Gregor 27/1/2015)
Hilbert schemes of points: generalities on construction
on a K3, holomorphic symplectic structure (see Beauville)
Talk 8 (Michael 3/2/2015)
intro to moduli of sheaves
From Huybrechts and Lehn's book and Mukai's papers
Talk 9 (?? 10/2/2015)
??
From here on we can see what everyone is interested in. Some options are:
Bayer-Macri: get a feeling for the geometry here
Charles and Markman on the standard conjectures for IHSMs
Markman and Mehrotra density of Hilbert schemes of points
LMMP for ihsms
Markman's lagrangian fibrations paper
Results on cones: Amerik and Verbitsky's paper or Markman and Yoshioka
O'Grady's examples
Various Papers
Amerik and Verbitsky ``Rational curves on hyperkahler manifolds''
Bayer and Macri ``MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations'' Has nice summary of results on hyperkahler stuff
Beauville ``Varietes Kahleriennes dont la premiere classe de Chern est nulle''
Charles and Markman ``The Standard Conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K3 surfaces''
Charles and Pacienza ``Families of rational curves on holomorphic symplectic varieties''
Huybrechts ``Compact hyperkahler manifolds: Basic results''
Huybrechts ``A global Torelli theorem for hyperkaehler manifolds (after Verbitsky)''
Markman ``Lagrangian fibrations of holomorphic-symplectic varieties of K3^[n]-type''
Markman and Mehrotra ``Hilbert schemes of K3 surfaces are dense in moduli''
Markman and Yoshioka ``A proof of the Kawamata-Morrison Cone Conjecture for holomorphic symplectic varieties of K3^[n] or generalized Kummer deformation type''
Mukai ``Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''
Mukai ``Moduli of vector bundles on K3 surfaces, and symplectic manifolds''
Mukai ``On the moduli space of bundles on K3 surfaces I''
Namikawa ``Deformation theory of singular symplectic n-folds''
O'Grady ``A new six-dimensional irreducible symplectic variety''
O'Grady ``Desingularized moduli spaces of sheaves on a K3''
Yoshioka ``Irreducibility of moduli spaces of vector bundles on K3 surfaces''
Various Notes
Huybrechts ``Compact hyperkahler manifolds notes'' (see also book with Gross and Joyce)
Huybrechts ``Hyperkahler manifolds and sheaves''
Huybrechts ``Compact Hyperkahler manifolds'' Contains more details than the paper.
O'Grady ``Compact Hyperkahler manifolds: an introduction''