{"id":{"repo_id":"cornell","oai_identifier":"oai:ecommons.cornell.edu:1813/117626"},"canonical_url":"https://search.dev.ndltd.org/etd/cornell/oai:ecommons.cornell.edu:1813/117626","repository":{"repo_id":"cornell","name":"Cornell University","base_url":"https://ecommons.cornell.edu/server/oai/request"},"display":{"title":"Limits of stability conditions and their geometry","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Robotis, Alekos"],"institution":"Cornell University","degree_name":"Ph. 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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."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Limits of stability conditions and their geometry"]}]}],"canonical_facts":{"dc:contributor.committeemember":["Knutson, Allen","Riley, Tara"],"dc:creator":["Robotis, Alekos"],"dc:date.accessioned":["2025-08-21T14:14:09Z"],"dc:date.available":["2025-08-21T14:14:09Z"],"dc:date.issued":["2025-05"],"dc:description":["171 pages"],"dc:description.abstract":["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. 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