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Wall crossing for quasimaps and representations of symmetric groups

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EMGW05 - Moduli stacks and enumerative geometry

The notion of quasimaps is a generalization of Kontsevich-Manin’s stable maps to GIT quotients and allows us to consider a variety of stability conditions. From the beginning of Gromov-Witten theory, quasimaps played a key role and it turned out to be quite fruitful to study wall crossing of moduli spaces of quasimaps. In this talk, we will look into Le Potier’s stability for quasimaps and find that the wall crossing gives us a new construction of the moduli spaces of pointed rational curves. Using this, we can effectively compute the characters of their cohomology by the symmetric group action which permutes the marked points. As a consequence, we can show that the invariant cohomology is asymptotically log-concave but not strongly log-concave.  Based on joint work with Jinwon Choi and Donggun Lee.

This talk is part of the Isaac Newton Institute Seminar Series series.

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