Date of Award

2019

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Mathematics

First Advisor

Tony Pantev

Abstract

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

Share

COinS