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Seminar in Algebraic Geometry: “Different extensions of the double ramification cycles”

Friday, May 17th, 2019, 9:30 - Room 1AD100 - Nicola Pagani

ARGOMENTI: Seminars

“Different extensions of the double ramification cycles”
Friday, May 17th, 2019, 9:30
Room 1AD100
Nicola Pagani (Liverpool)

Abstract
Fix natural numbers g,n and integers d1, d2, ..., dn. The moduli space Mgn of n-pointed curves of genus g contains an interesting locus that parameterises pointed curves (C, p1, ..., pn) that admit a meromorphic function f such that div(f) equals \sum di pi. There is different ways of extending this cycle to the compactification of Mgn by means of stable n-pointed curves of arithmetic genus g. One way of extending this cycle is by means of the theory of relative stable maps, and another is by pulling back the Brill-Noether class w^0_0 via a (possibly rational) section to some compactified universal Jacobian. In this talk I will explain how the first can be seen as a particular case of the second (a joint work with David Holmes and Jesse Kass). If the ramification vector is of type (1, -1, 0,...0) then this gives an (unexpected to me) relation between two tautological classes.