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math.AG2011
Coherent Sheaves on Quiver Varieties and Categorification
Sabin Cautis, Joel Kamnitzer, Anthony Licata
We construct geometric categorical Lie algebra actions on the derived category of coherent sheaves on Nakajima quiver varieties. These actions categorify Nakajima's construction of…
math.AG2007
The Abelian Monodromy Extension Property for Families of Curves
Sabin Cautis
Necessary and sufficient conditions are given (in terms of monodromy) for extending a family of smooth curves over an open subset U of S to a family of stable curves over S. More p…
math.AG2007
Knot homology via derived categories of coherent sheaves I, sl(2) case
Sabin Cautis, Joel Kamnitzer
Using derived categories of equivariant coherent sheaves, we construct a categorification of the tangle calculus associated to sl(2) and its standard representation. Our constructi…