TY - JOUR
T1 - Crepant resolutions of weighted projective spaces and quantum deformations
JF - 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)
Y1 - 2011
A1 - Samuel Boissiere
A1 - Etienne Mann
A1 - Fabio Perroni
AB - 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.
PB - SISSA
UR - http://hdl.handle.net/1963/6514
N1 - 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)
U1 - 6463
U2 - Mathematics
U4 - 1
U5 - MAT/03 GEOMETRIA
ER -
TY - JOUR
T1 - A model for the orbifold Chow ring of weighted projective spaces
JF - Comm. Algebra 37 (2009) 503-514
Y1 - 2009
A1 - Samuel Boissiere
A1 - Etienne Mann
A1 - Fabio Perroni
AB - 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.
PB - Taylor and Francis
UR - http://hdl.handle.net/1963/3589
U1 - 711
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - The cohomological crepant resolution conjecture for P(1,3,4,4)
Y1 - 2007
A1 - Samuel Boissiere
A1 - Fabio Perroni
A1 - Etienne Mann
AB - 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.
PB - SISSA
UR - http://hdl.handle.net/1963/6513
N1 - 11 pages, 1 figure
U1 - 6464
U2 - Mathematics
U4 - 1
U5 - MAT/03 GEOMETRIA
ER -
TY - RPRT
T1 - Smooth toric DM stacks
Y1 - 2007
A1 - Barbara Fantechi
A1 - Etienne Mann
A1 - Fabio Nironi
AB - We give a new definition of smooth toric DM stacks in the same spirit of toric varieties. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks.
UR - http://hdl.handle.net/1963/2120
U1 - 2123
U2 - Mathematics
U3 - Mathematical Physics
ER -