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SUMMARY:Newton-Okounkov bodies and Picard numbers on surfaces
DTSTART;VALUE=DATE-TIME:20230111T103000Z
DTEND;VALUE=DATE-TIME:20230111T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T101744Z
UID:indico-event-8754@cern.ch
DESCRIPTION:Abstract: In this talk\, we will discuss a preprint of\nFerná
ndez-Nickel-Roé 'Newton-Okounkov bodies and Picard numbers on surfaces'\
nhttps://arxiv.org/pdf/2101.05338v1.pdf\n\nNewton–Okounkov bodies were i
ntroduced by A. Okounkov as a tool in\nrepresentation theory\; later Kaveh
-Khovanskii and Lazarsfeld-Mustata\ndeveloped a general theory with applic
ations to both convex and algebraic\ngeometry. In this preprint\, the auth
ors study the shapes of all\nNewton-Okounkov bodies of a given big divisor
on a surface S with respect\nto all rank 2 valuations of K(S). They obtai
n upper bounds for\, and in\nmany cases determine exactly\, the possible n
umbers of vertices of these\nbodies. The upper bounds are expressed in ter
ms of Picard numbers. They\nalso conjecture that the set of all Newton-Oko
unkov bodies of a single\nample divisor determines the Picard number of S\
, and proves that this is\nthe case for Picard number 1\, by an explicit c
haracterization of surfaces\nof Picard number 1 in terms of Newton-Okounko
v bodies.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId
=8754
LOCATION: AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8754
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