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BEGIN:VTIMEZONE
TZID:Asia/Seoul
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TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20240101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250520T110000
DTEND;TZID=Asia/Seoul:20250520T120000
DTSTAMP:20260503T074918
CREATED:20250425T013616Z
LAST-MODIFIED:20250425T013616Z
UID:3784-1747738800-1747742400@ccg.ibs.re.kr
SUMMARY:Gian Pietro Pirola\, Asymptotic directions on the moduli space of curves
DESCRIPTION:    Speaker\n\n\nGian Pietro Pirola\nUniversity of Pavia\n\n\n\n\n\n\nWe present some computational improvements that allow us to study asymptotic lines in the tangent of the moduli space Mg of the curves of genus g. The asymptotic directions are those tangent directions that are annihilated by the second fundamental form induced by the Torelli map. We give examples of asymptotic lines for any g > 3 and we study their rank. The rank r(v) of a tangent direction at Mg is defined to be the rank of the cup product map associated to the infinitesimal deformation map\, that is the infinitesimal variation of Hodge structure in that direction. We show that if v is not zero and r(v)< (cliff(C) + 1) where cliff(C) is the Clifford index of C\, then v is not asymptotic and we study the case when r(v)= cliff(C). Finally all asymptotic directions of rank 1 are determined and a description of the rank 2 case is given. It is a joint work with Elisabetta Colombo and Paola Frediani.
URL:https://ccg.ibs.re.kr/event/2025-0520-2/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Algebraic Geometry Seminar
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