Contractions of subcurves of families of log curves

Bozlee, Sebastian

doi:10.1080/00927872.2021.1925903

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Nonisolated Singularities1

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2022

2023

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Cited by 2 publications

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“…C in sufficiently general families. We wonder whether a pointwise construction might be possible, realising both steps as special instances of a more general pushout of logarithmic subcurves, in the spirit of S Bozlee [18].…”

Section: Nonisolated Singularitiesmentioning

confidence: 99%

A smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curves

Battistella¹,

Carocci²

2023

Geom. Topol.

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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.

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Section: Nonisolated Singularitiesmentioning

confidence: 99%