BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gerard Freixas (Ecole Polytechnique) DTSTART:20261023T150000Z DTEND:20261023T161500Z DTSTAMP:20261025T111745Z UID:CIRGET/171 DESCRIPTION:Title: A numerical obstruction to smooth fillings of Calabi-Yau degenerations\nby Gerard Freixas (Ecole Polytechnique) as part of CRM - Séminaire du CIRGET / Géométrie et Topologie\n\nLecture held in PK-5115.\n\nAbstract\ nIn a previous work with D. Eriksson and C. Mourougane\, we introduced a r eal valued invariant of Calabi-Yau manifolds\, based on the analytic torsi on of holomorphic differentials\, generalizing work of Fang\, Lu and Yoshi kawa in dimension 3. We call it the BCOV invariant. For one-parameter dege nerations\, we established the logarithmic divergence of the BCOV invarian t. It follows that the rate of logarithmic divergence is an obstruction to smooth fillings of such families. Recently\, in joint work with D. Erikss on\, we have considered the problem of effectively computing this obstruct ion. We obtain simple expressions for degenerations with isolated singular ities\, depending on Hodge theoretic invariants of the Milnor fiber. Numer ical experiments motivated us to conjecture that the obstruction is strict ly positive for isolated terminal singularities. This can be proven in sev eral instances\, covering in particular the ADE singularities. As a result \, Calabi-Yau degenerations with such singularities do not admit any smoot h fillings. This generalizes a result by Claire Voisin from 1990\, in the case of Lefschetz pencils of hypersurfaces (A_1 singularities)\, which was one of the few known results.\n LOCATION:https://researchseminars.org/talk/CIRGET/171/ END:VEVENT END:VCALENDAR