We construct a modular desingularisation of M_{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.

A smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curves / Battistella L.; Carocci F.. - In: GEOMETRY & TOPOLOGY. - ISSN 1364-0380. - STAMPA. - 27:3(2023), pp. 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

Battistella L.;
2023

Abstract

We construct a modular desingularisation of M_{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.
2023
A smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curves / Battistella L.; Carocci F.. - In: GEOMETRY & TOPOLOGY. - ISSN 1364-0380. - STAMPA. - 27:3(2023), pp. 1203-1272. [10.2140/gt.2023.27.1203]
Battistella L.; Carocci F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/952653
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