Homological mirror symmetry for higher dimensional pairs of pants
| Autor: | Alexander Polishchuk, Yanki Lekili |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
partially wrapped Fukaya category 01 natural sciences Mathematics - Algebraic Geometry Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Representation Theory (math.RT) 0101 mathematics higher-dimensional pairs of pants Algebraic Geometry (math.AG) Pair of pants Mathematics::Symplectic Geometry Mathematics Algebra and Number Theory Homological mirror symmetry symmetric products of surfaces 010102 general mathematics 16. Peace & justice Complement (complexity) Mathematics - Symplectic Geometry Symplectic Geometry (math.SG) modules over non-commutative orders 010307 mathematical physics Fukaya category Mathematics - Representation Theory |
| Zdroj: | Lekili, Y & Polishchuk, A 2020, ' Homological mirror symmetry for higher-dimensional pairs of pants ', COMPOSITIO MATHEMATICA, vol. 156, no. 7, pp. 1310-1347 . https://doi.org/10.1112/S0010437X20007150 |
| DOI: | 10.1112/S0010437X20007150 |
| Popis: | Using Auroux's description of Fukaya categories of symmetric products of punctured surfaces, we compute the partially wrapped Fukaya category of the complement of $k+1$ generic hyperplanes in $\mathbb{CP}^n$, for $k \geq n$, with respect to certain stops in terms of the endomorphism algebra of a generating set of objects. The stops are chosen so that the resulting algebra is formal. In the case of the complement of $(n+2)$-generic hyperplanes in $\mathbb{C}P^n$ ($n$-dimensional pair-of-pants), we show that our partial wrapped Fukaya category is equivalent to a certain categorical resolution of the derived category of the singular affine variety $x_1x_2..x_{n+1}=0$. By localizing, we deduce that the (fully) wrapped Fukaya category of $n$-dimensional pants is equivalent to the derived category of $x_1x_2...x_{n+1}=0$. We also prove similar equivalences for finite abelian covers of the $n$-dimensional pair-of-pants. 41 pages, 10 figures. Typographical edits. To appear in Compositio Mathematica |
| Databáze: | OpenAIRE |
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