BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Luca Battistella (University of Heidelberg) DTSTART:20200626T131500Z DTEND:20200626T141500Z DTSTAMP:20260422T172352Z UID:TGiZ/8 DESCRIPTION:Title: A s mooth compactification of genus two curves in projective space\nby Luc a Battistella (University of Heidelberg) as part of Tropical Geometry in F rankfurt/Zoom TGiF/Z\n\n\nAbstract\nQuestions of enumerative geometry can often be translated into problems of intersection theory on a compact modu li space of curves in projective space. Kontsevich's stable maps work extr aordinarily well when the curves are rational\, but in higher genus the bu rden of degenerate contributions is heavily felt\, as the moduli space acq uires several boundary components. The closure of the locus of maps with s mooth source curve is interesting but troublesome\, for its functor of poi nts interpretation is most often unclear\; on the other hand\, after the w ork of Li--Vakil--Zinger and Ranganathan--Santos-Parker--Wise in genus one \, points in the boundary correspond to maps that admit a nice factorisati on through some curve with Gorenstein singularities (morally\, contracting any higher genus subcurve on which the map is constant). The question bec omes how to construct such a universal family of Gorenstein curves. In joi nt work with F. Carocci\, we construct one such family in genus two over a logarithmic modification of the space of admissible covers. I will focus on how tropical geometry determines this logarithmic modification via trop ical canonical divisors.\n LOCATION:https://researchseminars.org/talk/TGiZ/8/ END:VEVENT END:VCALENDAR