Limits of stability conditions and their geometry

After giving a brief survey of the study of derived categories in algebraic geometry, I present a pair of research papers. The first, joint with Daniel Halpern-Leistner and Jeffrey Jiang, introduces the notion of quasi-convergent paths in the space of stability conditions. We prove that quasi-convergent paths give rise to decompositions of triangulated categories (e.g. derived categories of coherent sheaves on a variety) and that conversely for a smooth and proper dg-category all polarized semiorthogonal decompositions arise in this fashion. In the second paper, I study the geometry of certain moduli spaces of genus 0 curves with differentials called multiscale lines which were introduced in joint work with Daniel Halpern-Leistner. I prove that these spaces are complex projective varieties by giving an explicit isomorphism with a blow-up of a linear subspace arrangement of projective space. I use this isomorphism to connect these spaces of multiscale lines with other spaces in the literature studied by Zahariuc.

Name thesis:degree_name

Ph. D., Mathematics

Level thesis:degree_level

Doctor of Philosophy

Discipline thesis:degree_discipline

Mathematics

Grantor

Cornell University

Year dc:date.issued

2025

Author dc:creator

• Robotis, Alekos

Committee members dc:contributor.committeemember

• Knutson, Allen
• Riley, Tara

• Algebraic geometry
• Derived categories
• Moduli of curves

Statement dc:rights

• Attribution 4.0 International

Licence dc:rights.uri

• https://creativecommons.org/licenses/by/4.0/

Language dc:language.iso

en

DOI

https://doi.org/10.7298/f3ym-e856

Dc Identifier Other

ProQuest Submission ID: 14931
ProQuest Publication ID: 31999273

OAI identifier oai:identifier

oai:ecommons.cornell.edu:1813/117626