2017/06/26 by Samuel Bach, Bach, Samuel, Valerio Melani +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.AG #math.SG
paper · pdf · doi:10.48550/arxiv.1706.08369
17 pages
arxiv created 2020/05/09 · arxiv updated 2020/05/12
We introduce and study the derived moduli stack Symp(X,n) of n-shifted symplectic structures on a given derived stack X, as introduced by [PTVV] (IHES Vol. 117, 2013). In particular, under reasonable assumptions on X, we prove that Symp(X, n) carries a canonical shifted quadratic form. This generalizes a classical result of Fricke and Habermann, which was established in the C∞-setting, to the broader context of derived algebraic geometry, thus proving a conjecture stated by Vezzosi.