Bridgeland-stable moduli spaces for $K$-trivial surfaces

Arcara, Daniele, and Bertram, Aaron. "Bridgeland-stable moduli spaces for $K$-trivial surfaces." Journal of the European Mathematical Society 015.1 (2013): 1-38. <http://eudml.org/doc/277696>.

@article{Arcara2013,
abstract = {We give a one-parameter family of Bridgeland stability conditions on the derived category of a smooth projective complex surface $S$ and describe “wall-crossing behavior” for objects with the same invariants as $\mathcal \{O\}_C(H)$ when $H$ generates Pic$(S)$ and $C\in \left|H\right|$. If, in addition, $S$ is a $K3$ or Abelian surface, we use this description to construct a sequence of fine moduli spaces of Bridgeland-stable objects via Mukai flops and generalized elementary modifications of the universal coherent sheaf. We also discover a natural generalization of Thaddeus’ stable pairs for curves embedded in the moduli spaces.},
author = {Arcara, Daniele, Bertram, Aaron},
journal = {Journal of the European Mathematical Society},
keywords = {Bridgeland stability condition; derived category; stable objects; moduli space; $K3$ surface; abelian surface; Mukai flops; Bridgeland stability condition; derived category; stable objects; moduli space; surface; abelian surface; Mukai flops},
language = {eng},
number = {1},
pages = {1-38},
publisher = {European Mathematical Society Publishing House},
title = {Bridgeland-stable moduli spaces for $K$-trivial surfaces},
url = {http://eudml.org/doc/277696},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Arcara, Daniele
AU - Bertram, Aaron
TI - Bridgeland-stable moduli spaces for $K$-trivial surfaces
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 1
SP - 1
EP - 38
AB - We give a one-parameter family of Bridgeland stability conditions on the derived category of a smooth projective complex surface $S$ and describe “wall-crossing behavior” for objects with the same invariants as $\mathcal {O}_C(H)$ when $H$ generates Pic$(S)$ and $C\in \left|H\right|$. If, in addition, $S$ is a $K3$ or Abelian surface, we use this description to construct a sequence of fine moduli spaces of Bridgeland-stable objects via Mukai flops and generalized elementary modifications of the universal coherent sheaf. We also discover a natural generalization of Thaddeus’ stable pairs for curves embedded in the moduli spaces.
LA - eng
KW - Bridgeland stability condition; derived category; stable objects; moduli space; $K3$ surface; abelian surface; Mukai flops; Bridgeland stability condition; derived category; stable objects; moduli space; surface; abelian surface; Mukai flops
UR - http://eudml.org/doc/277696
ER -