%0 Journal Article %J 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) %D 2011 %T Crepant resolutions of weighted projective spaces and quantum deformations %A Samuel Boissiere %A Etienne Mann %A Fabio Perroni %X 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. %B 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) %I SISSA %G en %U http://hdl.handle.net/1963/6514 %1 6463 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Fabio Perroni (perroni@sissa.it) on 2013-02-28T17:54:00Z\nNo. of bitstreams: 1\nmath_0610617v2.pdf: 309225 bytes, checksum: 1488b79e5765bdffd4353bd8e04ffa8e (MD5) %0 Journal Article %J Comm. Algebra 37 (2009) 503-514 %D 2009 %T A model for the orbifold Chow ring of weighted projective spaces %A Samuel Boissiere %A Etienne Mann %A Fabio Perroni %X We construct an isomorphism of graded Frobenius algebras between the orbifold Chow ring of weighted projective spaces and graded algebras of groups of roots of the unity. %B Comm. Algebra 37 (2009) 503-514 %I Taylor and Francis %G en_US %U http://hdl.handle.net/1963/3589 %1 711 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-03-09T14:26:00Z\\nNo. of bitstreams: 1\\n0709.4559v1.pdf: 182412 bytes, checksum: d6f5ea45f21c8eb995d417277fa544d4 (MD5) %R 10.1080/00927870802248902 %0 Journal Article %D 2007 %T The cohomological crepant resolution conjecture for P(1,3,4,4) %A Samuel Boissiere %A Fabio Perroni %A Etienne Mann %X 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. %I SISSA %G en %U http://hdl.handle.net/1963/6513 %1 6464 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Fabio Perroni (perroni@sissa.it) on 2013-02-28T17:55:28Z\nNo. of bitstreams: 1\n0712.3248v1.pdf: 182952 bytes, checksum: a5a581e6ba586472b9418608365283cf (MD5)