Twisted Stability and Fourier–Mukai Transform I
By K. Yoshioka. Compositio Mathematica, 2001
64 citations recorded by the source corpus.
In this paper, we consider the preservation of stability by using the notion of twisted stability. As applications, (1) we show that moduli spaces of stable sheaves on K3 and abelian surfaces are irreducible and (2) we compute Hodge polynomials of some moduli spaces of stable sheaves on Enriques surfaces.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/89ac34b0523d1a50d6835cd080c5ebc453181d13
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Citations in the corpus
- Moduli of twisted sheaves (2004, methodology): “polynomial of a torsion free sheaf Fone computes the Hilbert polynomial of F⊗O(α), where αis some Q-divisor (with stability now being called “α-twisted stability”). We refer the reader to their work ([61] and the references therein) for a detailed description of the situation (in characteristic 0); ”
- Singular symplectic moduli spaces (2005, background): “This theorem is due to Yoshioka [28] in the case of torsion free sheaves.”
- Projectivity and birational geometry of Bridgeland moduli spaces on an Enriques surface (2014, methodology): “These auto-equivalences were referred to as Fourier–Mukai transforms associated to (−1)-reflection in [52] and modular reflections in [54], but the above interpretation strengthens and elucidates the connection with the covering spherical twist on the K3 surface Ỹ .”
- Moduli spaces of twisted sheaves on a projective variety (2004, background): “3.4. Let vG:= (r,ζ,b) be a Mukai vector with r,hv2 Gi >0 which is not necessary primitive. By the same proof, we can also show that MY,G H (vG) is an irreducible normal variety for a general H(cf. [Y2]). 3.3. The second cohomology groups of moduli spaces. By Theorem 3.16, MY,G H (vG) is an irredu”
- Twisted sheaves and the period-index problem (2005, methodology): “he abelian category of right A-modules, where A = Hom(V ,V ). Alternatively, one can give a cocyclic description of twisted sheaves (used by C˘alda˘raru in his thesis [2], Yoshioka in his recent work [47], and others of a mathematico-physical bent) as follows: choose a hypercovering U• →X with a 2-c”