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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20210101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20221027T110000
DTEND;TZID=Asia/Seoul:20221027T120000
DTSTAMP:20260420T144912
CREATED:20220907T075418Z
LAST-MODIFIED:20221011T102020Z
UID:1701-1666868400-1666872000@ccg.ibs.re.kr
SUMMARY:Jaewoo Jeong\, Hankel Index of Smooth Non-ACM Curves of Almost Minimal Degree
DESCRIPTION:     Speaker\n\n\nJaewoo Jeong IBS CCG\n\n\n\n\n \nThe Hankel index of a real variety is a semi-algebraic invariant that quantifies the (structural) difference between nonnegative quadrics and sums of squares on the variety. Note that the Hankel index of a variety is difficult to compute and was computed for just few cases. In 2017\, Blekherman\, Sinn\, and Velasco provided an captivating (lower) bound of the Hankel index of a variety by an algebraic invariant\, Green-Lazarsfeld index\, of the variety. In particular\, if the variety X is an arithmetrically Cohen-Macaulay (ACM) variety of almost minimal degree\, then the Hankel index of X equals to the Green-Lazarsfeld index of X plus one (which is the equality case of the bound). We study the Hankel index of smooth non-ACM curves of almost minimal degree. Note that the curve is the image of the projection of rational normal curves away from an outer point. It is known that the Green-Lazarsfeld index of the curve is determined by the rank of the center of the projection with respect to the rational normal curve. We found a new rank of the center that detects the Hankel index of the rational curves. In addition\, it turns out that the rational curves are the first class of examples that the lower bound of the Hankel index is strict.
URL:https://ccg.ibs.re.kr/event/2022-10-27/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
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