Geodesic
The derived moduli stack of shifted symplectic structures
Bach, Samuel1 ; Melani, Valerio2 
1 University of British Columbia, Vancouver, Canada
2 Università di Pisa, Italy and Università di Milano, Italy
Rendiconti del Seminario Matematico della Università di Padova, Tome 141 (2019), pp. 221-241

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We introduce and study the derived moduli stack 𝐒𝐲𝐦𝐩(X,n) of n-shifted symplectic structures on a given derived stack X, as introduced in [8]. In particular, under reasonable assumptions on X, we prove that 𝐒𝐲𝐦𝐩(X,n) carries a canonical quadratic form, in the sense of [14]. This generalizes a classical result of Fricke and Habermann (see [13]), which was established in the C ∞ -setting, to the broader context of derived algebraic geometry, thus proving a conjecture stated in [14].

Publié le :
DOI : 10.4171/RSMUP/24
Classification : 14, 53
Mots-clés : Derived algebraic geometry, moduli spaces, Lie algebroids, shifted symplectic structures

Bach, Samuel 1 ; Melani, Valerio 2

1 University of British Columbia, Vancouver, Canada
2 Università di Pisa, Italy and Università di Milano, Italy 
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     title = {The derived moduli stack of shifted symplectic structures},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {221--241},
     publisher = {European Mathematical Society Publishing House},
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     year = {2019},
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Bach, Samuel; Melani, Valerio. The derived moduli stack of shifted symplectic structures. Rendiconti del Seminario Matematico della Università di Padova, Tome 141 (2019), pp. 221-241. doi: 10.4171/RSMUP/24

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