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SUMMARY:Abundance Conjecture on Uniruled Varieties
DTSTART;VALUE=DATE-TIME:20220920T103000Z
DTEND;VALUE=DATE-TIME:20220920T113000Z
DTSTAMP;VALUE=DATE-TIME:20230130T022952Z
UID:indico-event-8559@cern.ch
DESCRIPTION:Abstract: This content of this talk is a paper of Valdimir Laz
ic. Abundance conjecture says that if X is a smooth projective variety suc
h that its canonical divisor K_X is nef\, i.e. K_X intersects every curve
non-negatively\, then there is a positive integer m such that the m-th ten
sor power of the canonical line bundle \\omega_X^{\\otimes m}\\cong \\math
cal{O}_X(mK_X) has non-zero global sections\, and moreover\, these global
sections generate the line bundle \\omega_X^{\\otimes m}. In particular\,
there is a projective morphism f:X\\to \\mathbb{P}^N to a porjective space
determined by global sections of \\omega_X^{\\otimes m}. This morphism al
lows X to be seen as a fibration of Calabi-Yau varieties (i.e. varieties w
hose canonical classes are trivial). The Abudance conjecture is one of mos
t important outstanding conjecture in the minimal model program. In the pa
per titled ‘’Abundance for Uniruled Varieties which are not Rationally
Connected’’\, Lazic shows that if (X\, B) is a klt pair of dimension
n such that X is uniruled but not rationally connected\, and if we assume
that the minimal model program holds in dimension n-1\, then the Abundance
conjecture holds for (X\, B) is dimension n. In my talk I will explain th
e main ideas and techniques of Lazic’s proof.\n\nhttps://indico.tifr.res
.in/indico/conferenceDisplay.py?confId=8559
LOCATION: AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8559
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