University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2019 On The Compatibility Of Derived Structures On Critical Loci Antonijo Mrcela University of Pennsylvania,
[email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Mathematics Commons Recommended Citation Mrcela, Antonijo, "On The Compatibility Of Derived Structures On Critical Loci" (2019). Publicly Accessible Penn Dissertations. 3441. https://repository.upenn.edu/edissertations/3441 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/3441 For more information, please contact
[email protected]. On The Compatibility Of Derived Structures On Critical Loci 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 w∈?(S) and as the critical locus of the restriction w|ₓ∈?(X) for some smooth subscheme X⊂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 X⊂S is a general closed embedding. Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Mathematics First Advisor Tony Pantev Keywords Batalin–Vilkovisky formalism, compatibility of derived structures,