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Systolic inequalities for K3 surfaces via stability conditions

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 نشر من قبل Yu-Wei Fan
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English
 تأليف Yu-Wei Fan




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We introduce the notions of categorical systoles and categorical volumes of Bridgeland stability conditions on triangulated categories. We prove that for any projective K3 surface, there exists a constant C depending only on the rank and discriminant of its Picard group, such that $$mathrm{sys}(sigma)^2leq Ccdotmathrm{vol}(sigma)$$ holds for any stability condition on the derived category of coherent sheaves on the K3 surface. This is an algebro-geometric generalization of a classical systolic inequality on two-tori. We also discuss applications of this inequality in symplectic geometry.



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