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

Battistella, LucaCarocci, Francesca2023-08-142023-08-142023-08-142023-01-0110.2140/gt.2023.27.1203https://infoscience.epfl.ch/handle/20.500.14299/199755WOS:001021179100005We 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.Mathematicsgromov-witten invariantspointed elliptic-curvesmodular compactificationsstable mapssingularitiesdeformationenumerationstacksA smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curvestext::journal::journal article::research article