Carissimi,
vi segnalo questi due seminari, che si terranno entrambi domani.
Cari saluti,
Filippo
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giovedi` 31 maggio ore 15 aula seminari
Luca Battistella
Relative quasimaps and quasimap quantum Lefschetz
Quasimaps provide a compactification of the space of maps from smooth
curves to a GIT quotient; Ciocan-Fontanine and Kim used them to prove
beautiful wall-crossing formulae, comparing the resulting invariants with
ordinary Gromov-Witten ones. In joint work with Navid Nabijou, we introduce
the notion of genus zero relative quasimaps to a toric target X with
respect to a smooth (but not necessarily toric) hyperplane section Y,
extending work of Gathmann to this setting. Increasing the tangency
requirement gives us smaller and smaller moduli spaces; their virtual
classes are related by a simple recursion formula. Gathmann's inductive
algorithm allows us to compute restricted invariants of Y from those of X.
Under some positivity assumption, this can be made into a compact formula
for generating series of quasimap invariants, which recovers a result of
Ciocan-Fontanine and Kim. We are working towards an extension of this
approach to reduced genus one invariants.
giovedi` 31 maggio ore 16 aula seminari
Giovanni Inchiostro
Moduli of Weierstrass fibrations.
We study the the moduli space of KSBA stable pairs (X,sS+\sum a_i F_i),
consisting of a Weierstrass fibration X, its section S, and some fibers
F_i. We find a compactification which is a DM stack, and we prove that
there are wall-crossing morphisms when the weights s and a_i change. This
recovers the work of Ascher and Bejleri in the case in which s=1 and the
one of La Nave when s=1 and a_i=0.
