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SUMMARY:Navid Nabijou (Imperial college): Relative quasimaps and a quantum
Lefschetz theorem
DTSTART;VALUE=DATE-TIME:20180427T120000Z
DTEND;VALUE=DATE-TIME:20180427T130000Z
DTSTAMP;VALUE=DATE-TIME:20190617T030908Z
UID:indico-event-3275@indico.math.cnrs.fr
DESCRIPTION:The theory of stable quasimaps is an important tool in modern
enumerative geometry\, providing an alternative system of curve counts to
the usual Gromov-Witten invariants. In joint work with Luca Battistella\,
we define moduli spaces of relative stable quasimaps to a pair (X\,Y)\, wh
ere Y is a hyperplane section in X. Intuitively these spaces parametrise q
uasimaps in X with specified orders of tangency with Y\, and can be used t
o define relative quasimap invariants. By investigating these moduli space
s we obtain a quantum Lefschetz formula\, expressing the quasimap invarian
ts of Y in terms of the invariants of X. Since the I-function from mirror
symmetry is equal to a generating function for these quasimap invariants\,
this result can be viewed as a “quantum Lefschetz theorem for I-functio
ns.” It also agrees with an earlier formula obtained by Ciocan-Fontanine
and Kim.\n\nhttps://indico.math.cnrs.fr/event/3275/
LOCATION:Angers I 001
URL:https://indico.math.cnrs.fr/event/3275/
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