D0-brane realizations of the resolution of a reduced singular curve

Chien-Hao Liu Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43717

arXiv preprint arXiv:1111.4707, 2011.11
Based on examples from superstring/D-brane theory since the work of Douglas and Moore on resolution of singularities of a superstring target-space Y via a D-brane probe, the richness and the complexity of the stack of punctual D0-branes on a variety, and as a guiding question, we lay down a conjecture that any resolution Y of a variety Y over Y can be factored through an embedding of Y into the stack Y of punctual D0-branes of rank Y on Y for Y in Y , where Y depends on the germ of singularities of Y . We prove that this conjecture holds for the resolution Y of a reduced singular curve Y over Y . In string-theoretical language, this says that the resolution Y of a singular curve Y always arises from an appropriate D0-brane aggregation on Y and that the rank of the Chan-Paton module of the D0-branes involved can be chosen to be arbitrarily large.
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  title={D0-brane realizations of the resolution of a reduced singular curve},
  author={Chien-Hao Liu, and Shing-Tung Yau},
  booktitle={arXiv preprint arXiv:1111.4707},
Chien-Hao Liu, and Shing-Tung Yau. D0-brane realizations of the resolution of a reduced singular curve. 2011. In arXiv preprint arXiv:1111.4707. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205205011281281.
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