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A
smooth compactification of the space of genus two curves in
projective space: via logarithmic geometry and Gorenstein
curves
Luca Battistella and Francesca Carocci |
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Geometry & Topology 27 (2023) 1203–1272
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Abstract |
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We construct a modular desingularisation of . The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers; with this enhanced logarithmic structure, it is possible to desingularise the main component by means of a logarithmic modification. Both isolated and nonreduced singularities appear naturally. Our construction gives rise to a notion of reduced Gromov–Witten invariants in genus two. |
Keywords
curves of genus two, Gorenstein curves, Vakil–Zinger,
desingularisation, moduli space, reduced Gromov–Witten
invariants
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Mathematical Subject Classification
Primary: 14H10
Secondary: 14H45, 14N35, 14T90
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References |
Publication
Received: 10 January 2021
Revised: 12 August 2021
Accepted: 10 September 2021
Published: 8 June 2023
Proposed: Dan Abramovich
Seconded: Mark Gross, Richard P Thomas
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Authors |
| Luca Battistella | |
| Humboldt-Universität zu Berlin Institut für Mathematik Berlin Germany |
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| Francesca Carocci | |
| Institute of Mathematics École Polytechnique Fédérale de Lausanne Lausanne Switzerland |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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