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A universal formula for counting cubic surfaces

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dc.contributor.authorDeopurkar, Ananden
dc.contributor.authorPatel, Ananden
dc.contributor.authorTseng, Dennisen
dc.date.accessioned2026-08-13T19:40:54Z
dc.date.available2026-08-13T19:40:54Z
dc.date.issued2026en
dc.description.abstractUsing equivariant geometry, we find a universal formula that computes the number of times a general cubic surface arises in a family. As sample applications, we show that the PGL4 orbit closure of a generic cubic surface has degree 96120, and that a general cubic surface arises 42120 times as a hyperplane section of a general cubic threefold.en
dc.description.sponsorshipAnand D. thanks the Australian Research Council for the grant DE180101360 that supported a part of this project.en
dc.description.statusPeer-revieweden
dc.format.extent40en
dc.identifier.issn2313-1691en
dc.identifier.scopus105036425129en
dc.identifier.urihttps://hdl.handle.net/1885/733814255
dc.language.isoenen
dc.rightsPublisher Copyright: © The Author(s), 2026.en
dc.sourceAlgebraic Geometryen
dc.subjectcubic surfacesen
dc.subjectenumerative geometryen
dc.subjectequivariant geometryen
dc.subjectmoduli theoryen
dc.titleA universal formula for counting cubic surfacesen
dc.typeJournal articleen
dspace.entity.typePublicationen
local.bibliographicCitation.lastpage450en
local.bibliographicCitation.startpage411en
local.contributor.affiliationDeopurkar, Anand; Mathematical Sciences Institute Research, Mathematical Sciences Institute, ANU College of Systems and Society, The Australian National Universityen
local.contributor.affiliationPatel, Anand; Oklahoma State Universityen
local.identifier.citationvolume13en
local.identifier.doi10.14231/AG-2026-012en
local.identifier.pure9864534d-a9a2-426f-9ee8-c6c53ef9e24aen
local.identifier.urlhttps://www.scopus.com/pages/publications/105036425129en
local.type.statusPublisheden

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