Timeline for The class of the diagonal in the symmetric product of a smooth curve

9 events

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Apr 7, 2016 at 11:03	history	edited	Jason Starr	CC BY-SA 3.0	added 189 characters in body
Apr 7, 2016 at 8:50	comment	added	Francesco Polizzi		Actually, at least in the case $d=g$ the result also follows from Mattuck's paper On symmetric product of curves. In fact, equations $(1)$ and $(5)$ of such a paper read $$2S+ \Delta_1 \cong 2 \sum _{1}^{2g-2}X[\mathfrak{p}_i], \quad \pi^{-1}(W_1)=S+X_1,$$ where $\mathfrak{p}_1+ \cdots +\mathfrak{p}_{2g-2} \in \|K_C\|$ and $S$ is the unique positive $g-1$ cycle in the canonical system of $\textrm{Sym}^g(C)$. Passing to algebraic equivalence and switching to our notation: $$2 S + \delta = (4g-4)x, \quad \theta = S+x,$$ hence $$\delta = 2((2g-1)x - \theta)$$ i.e. the desired formula when $d=g$.
Mar 30, 2016 at 16:39	history	edited	Jason Starr	CC BY-SA 3.0	added 986 characters in body
Mar 30, 2016 at 15:31	history	edited	Jason Starr	CC BY-SA 3.0	added 2 characters in body
Mar 30, 2016 at 15:14	history	edited	Jason Starr	CC BY-SA 3.0	added 812 characters in body
Mar 30, 2016 at 14:13	history	edited	Jason Starr	CC BY-SA 3.0	added 422 characters in body
Mar 30, 2016 at 13:31	vote	accept	Francesco Polizzi
S Mar 30, 2016 at 13:07	history	answered	Jason Starr	CC BY-SA 3.0
S Mar 30, 2016 at 13:07	history	made wiki			Post Made Community Wiki by Jason Starr