The non-equivariant coherent-constructible correspondence and a conjecture of King

Sarah Scherotzke ^[1] ; Nicolò Sibilla ^[2]
1. [1] University of Bonn
  
  University of Bonn
  
  Kreisfreie Stadt Bonn, Alemania
2. [2] University of British Columbia
  
  University of British Columbia
  
  Canadá
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 1, 2016, págs. 389-416
Idioma: inglés
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Resumen
- The coherent-constructible (CC) correspondence is a relationship between coherent sheaves on a toric variety X and constructible sheaves on a real torus TT . This was discovered by Bondal and established in the equivariant setting by Fang, Liu, Treumann, and Zaslow. In this paper, we explore various aspects of the non-equivariant CC correspondence. Also, we use the non-equivariant CC correspondence to prove the existence of tilting complexes in the derived categories of toric orbifolds satisfying certain combinatorial conditions. This has applications to a conjecture of King.