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Compactifications of Moduli of Points and Lines in the Projective Plane
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1496-7795
Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA.;HSE, Lab Algebra Geometry & Its Applicat, Moscow, Russia..
2021 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247Article in journal (Refereed) Published
Abstract [en]

Projective duality identifies the moduli spaces B-n and X(3, n) parametrizing linearly general configurations of n points in P-2 and n lines in the dual P-2, respectively. The space X(3, n) admits Kapranov's Chow quotient comp actification (X) over bar (3, n), studied also by Lafforgue, Hacking, Keel, Tevelev, and Alexeev, which gives an example of a KSBA moduli space of stable surfaces: it carries a family of certain reducible degenerations of P-2 with n "broken lines". Gerritzen and Piwek proposed a dual perspective, a compact moduli space parametrizing certain reducible degenerations of P-2 with n smooth points. We investigate the relation between these approaches, answering a question of Kapranov from 2003.

Place, publisher, year, edition, pages
Oxford University Press (OUP) , 2021.
National Category
Algebra and Logic Geometry Other Physics Topics
Identifiers
URN: urn:nbn:se:kth:diva-319015DOI: 10.1093/imrn/rnab200ISI: 000756700300001Scopus ID: 2-s2.0-85146453607OAI: oai:DiVA.org:kth-319015DiVA, id: diva2:1699233
Note

QC 20220927

Available from: 2022-09-27 Created: 2022-09-27 Last updated: 2023-06-08Bibliographically approved

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Schaffler, Luca

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