@article {2011,
	title = {Crepant resolutions of weighted projective spaces and quantum deformations},
	journal = {This article will be published in 2011 in the \"Nagoya Mathematical Journal\" Volume 201, March 2011, Pages 1-22, under the title \"Computing certain Gromov-Witten invariants of the crepant resolution of P{double-strock}(1, 3, 4, 4)},
	number = {arXiv:math/0610617;},
	year = {2011},
	note = {Exposition improved, new title, typos corrected. The section\r\n  concerning the model for the orbifold Chow ring has been removed (appears now\r\n  in our new preprint 0709.4559)},
	publisher = {SISSA},
	abstract = {We compare the Chen-Ruan cohomology ring of the weighted projective spaces\r\n$\\IP(1,3,4,4)$ and $\\IP(1,...,1,n)$ with the cohomology ring of their crepant\r\nresolutions. In both cases, we prove that the Chen-Ruan cohomology ring is\r\nisomorphic to the quantum corrected cohomology ring of the crepant resolution\r\nafter suitable evaluation of the quantum parameters. For this, we prove a\r\nformula for the Gromov-Witten invariants of the resolution of a transversal\r\n${\\rm A}_3$ singularity.},
	url = {http://hdl.handle.net/1963/6514},
	author = {Samuel Boissiere and Etienne Mann and Fabio Perroni}
}
@article {2007,
	title = {Chen-Ruan cohomology of ADE singularities},
	journal = {International Journal of Mathematics. Volume 18, Issue 9, October 2007, Pages 1009-1059},
	year = {2007},
	note = {This is a short version of my Ph.D. Thesis math.AG/0510528. Version\r\n  2: chapters 2,3,4 and 5 has been rewritten using the language of groupoids; a\r\n  link with the classical McKay correpondence is given. International Journal\r\n  of Mathematics (to appear)},
	publisher = {SISSA},
	abstract = {We study Ruan\'s \\textit{cohomological crepant resolution conjecture} for\r\norbifolds with transversal ADE singularities. In the $A_n$-case we compute both\r\nthe Chen-Ruan cohomology ring $H^*_{\\rm CR}([Y])$ and the quantum corrected\r\ncohomology ring $H^*(Z)(q_1,...,q_n)$. The former is achieved in general, the\r\nlater up to some additional, technical assumptions. We construct an explicit\r\nisomorphism between $H^*_{\\rm CR}([Y])$ and $H^*(Z)(-1)$ in the $A_1$-case,\r\nverifying Ruan\'s conjecture. In the $A_n$-case, the family\r\n$H^*(Z)(q_1,...,q_n)$ is not defined for $q_1=...=q_n=-1$. This implies that\r\nthe conjecture should be slightly modified. We propose a new conjecture in the\r\n$A_n$-case which we prove in the $A_2$-case by constructing an explicit\r\nisomorphism.},
	keywords = {Chen-Ruan cohomology, Ruan\'s conjecture, McKay correspondence},
	doi = {10.1142/S0129167X07004436},
	url = {http://hdl.handle.net/1963/6502},
	author = {Fabio Perroni}
}
@article {2007,
	title = {The cohomological crepant resolution conjecture for P(1,3,4,4)},
	number = {arXiv:0712.3248;},
	year = {2007},
	note = {11 pages, 1 figure},
	publisher = {SISSA},
	abstract = {We prove the cohomological crepant resolution conjecture of Ruan for the\r\nweighted projective space P(1,3,4,4). To compute the quantum corrected\r\ncohomology ring we combine the results of Coates-Corti-Iritani-Tseng on\r\nP(1,1,1,3) and our previous results.},
	url = {http://hdl.handle.net/1963/6513},
	author = {Samuel Boissiere and Fabio Perroni and Etienne Mann}
}
