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research article
A smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curves
January 1, 2023
We construct a modular desingularisation of (M) over bar (2,n)(P-r, d)(main). 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.
Type
research article
Web of Science ID
WOS:001021179100005
Authors
Publication date
2023-01-01
Publisher
Published in
Volume
27
Issue
3
Start page
1203
End page
1272
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
August 14, 2023
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