4 papers · 1 filter
Higher representation infinite algebras and toric Fano stacks of Picard number one or two
Ryu Tomonaga
Tilting bundles translate geometry into non-commutative algebra via derived equivalences. We prove the existence of, and classify, -tilting bundles consisting of line bundles on…
Non-commutative crepant resolutions of toric singularities with divisor class group of rank one
Ryu Tomonaga
We prove the existence and give a classification of toric non-commutative crepant resolutions (NCCRs) of Gorenstein toric singularities whose divisor class group has rank one. More…
On silting mutations preserving global dimension
Ryu Tomonaga
A -silting object is a silting object whose derived endomorphism algebra has global dimension or less. We give an equivalent condition, which can be stated in terms of dg qu…
Weak del Pezzo surfaces are characterized by the existence of -tilting bundles
Ryu Tomonaga
Tilting bundles provide a fundamental bridge between algebraic geometry and representation theory. For a tilting bundle on a smooth proper -dimensional variety, the global dimen…