Buongiorno,
Segnalo due seminari di geometria / algebra per domani pomeriggio. A presto,
Bruno
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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.
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