On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution

Chapter 1 Introduction......Page 8
Introduction to quivers......Page 12
The path algebra of a quiver......Page 14
Spaces of quiver representations......Page 17
The category of quiver representations......Page 20
Reflection functors......Page 21
Derksen-Weyman technique......Page 23
Domokos-Zubkov technique......Page 25
Schofield-van den Bergh technique......Page 27
Construction of filtered quiver varieties......Page 28
Quiver Grassmannians......Page 29
Quiver flag varieties......Page 30
Filtered quiver varieties......Page 31
Chapter 4 Categories of filtered and graded quiver varieties......Page 35
Filtered quiver varieties associated to finite type ADE Dynkin graphs......Page 48
(Framed) filtered quiver varieties associated to affine Dynkin type Ar......Page 55
Quivers with at most two pathways between any two vertices......Page 67
Other interesting family of quivers......Page 74
Comment regarding at most two pathways......Page 80
Introduction......Page 84
Moduli spaces......Page 86
Geometric invariant theory......Page 87
Hilbert schemes......Page 89
Hamiltonian reduction construction in symplectic geometry......Page 91
Grothendieck-Springer resolution......Page 94
The cotangent bundle of the enhanced Grothendieck-Springer resolution......Page 96
Hamiltonian reduction in stages......Page 99
Orthonormal projection operators in B......Page 101
On the fixed points by the Borel......Page 106
B-orbits on the rss-locus......Page 113
Proof of Proposition rss categorical quotient......Page 116
Changing coordinates......Page 118
B-invariant functions......Page 120
The initial ideal and regular sequence......Page 122
Proof of Proposition rss isomorphism of varieties......Page 123
Extension to a general flag......Page 124
m-Jordan quiver......Page 125
k-Kronecker quiver......Page 126
B-moment map......Page 127
P-moment map......Page 130
References......Page 132