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.
We classify the analytic germs of isolated Gorenstein curve singularities of genus three, and relate them to the connected components of strata of abelian differentials.
We classify the analytic germs of isolated Gorenstein curve singularities of genus three, and relate them to the connected components of strata of abelian differentials.
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