We construct a modular desingularisation of M2;n.Pr;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.
Battistella, L., Carocci, F. (2023). A smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curves. GEOMETRY & TOPOLOGY, 27(3), 1203-1272 [10.2140/gt.2023.27.1203].
A smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curves
Carocci F
2023-01-01
Abstract
We construct a modular desingularisation of M2;n.Pr;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.| File | Dimensione | Formato | |
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