Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)

Graduate Group


First Advisor

Tony Pantev


We study the problem of compatibility of derived structures on a scheme which can be presented as a critical locus in more than one way. We consider the situation when a scheme can be presented as the critical locus of a function wโˆˆ๐“ž(S) and as the critical locus of the restriction w|โ‚“โˆˆ๐“ž(X) for some smooth subscheme XโŠ‚S. In the case when S is the total space of a vector bundle over X, we prove that, under natural assumptions, the two derived structures coincide. We generalize the result to the case when X is a quantized cycle in S and also give indications how to proceed when XโŠ‚S is a general closed embedding.

Included in

Mathematics Commons