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X-WR-CALDESC:Events for Center for Complex Geometry
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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:20260503T061120
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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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250527T163000
DTEND;TZID=Asia/Seoul:20250527T173000
DTSTAMP:20260503T061120
CREATED:20250425T013928Z
LAST-MODIFIED:20250425T013928Z
UID:3786-1748363400-1748367000@ccg.ibs.re.kr
SUMMARY:Gian Pietro Pirola\, Sections of the Jacobian bundles of plane curves and applications
DESCRIPTION:    Speaker\n\n\nGian Pietro Pirola\nUniversity of Pavia\n\n\n\n\n\n\nWe study normal functions (sections of the Jacobian bundle) defined on the moduli space of pointed plane curves. Using the infinitesimal Griffiths invariant (refined by M. Green and C. Voisin) we show that a normal function with nontrivial but sufficiently “small” support cannot be “locally constant”. As an application\, we give a variational proof of the following result of Zu: \nTheorem: If C is a very general plane curve of degree d and C’ is any plane curve of degree d’\, then the cardinality i(C\, C’) of the intersection between C and C’ is > d-3. \nWe also show that if d > 3 and i(C\, C’) = d-2 then d’ = 1 and C’ is a bitangent or a flex line. For d = 4 this is a result of Chen\, Rield and Yeong. This is a joint work with Lorenzo Fassina.
URL:https://ccg.ibs.re.kr/event/2025-0527/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Algebraic Geometry Seminar
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