@article {2014,
title = {Pseudo-automorphisms of positive entropy on the blowups of products of projective spaces},
number = {Mathematische annalen;volume 359; issue 1-2; pages 189-209;},
year = {2014},
publisher = {Springer},
abstract = {We use a concise method to construct pseudo-automorphisms fn of the first dynamical degree d1(fn) > 1 on the blowups of the projective n-space for all n >= 2 and more generally on the blowups of products of projective spaces. These fn, for n=3 have positive entropy, and for n>= 4 seem to be the first examples of pseudo-automorphisms with d1(fn) > 1 (and of non-product type) on rational varieties of higher dimensions.},
doi = {10.1007/s00208-013-0992-4},
url = {http://urania.sissa.it/xmlui/handle/1963/34714},
author = {Fabio Perroni and Deqi Zhang}
}
@article {2013,
title = {Genus stabilization for moduli of curves with symmetries},
number = {arXiv:1301.4409;},
year = {2013},
note = {21 pages, 2 figures},
publisher = {SISSA},
abstract = {In a previous paper, arXiv:1206.5498, we introduced a new homological\r\ninvariant $\\e$ for the faithful action of a finite group G on an algebraic\r\ncurve.\r\n We show here that the moduli space of curves admitting a faithful action of a\r\nfinite group G with a fixed homological invariant $\\e$, if the genus g\' of the\r\nquotient curve is sufficiently large, is irreducible (and non empty iff the\r\nclass satisfies the condition which we define as \'admissibility\'). In the\r\nunramified case, a similar result had been proven by Dunfield and Thurston\r\nusing the classical invariant in the second homology group of G, H_2(G, \\ZZ).\r\n We achieve our result showing that the stable classes are in bijection with\r\nthe set of admissible classes $\\e$.},
keywords = {group actions, mapping class group, Moduli space of curves, Teichm{\"u}ller space},
url = {http://hdl.handle.net/1963/6509},
author = {Fabrizio Catanese and Michael L{\"o}nne and Fabio Perroni}
}
@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 {2009,
title = {A model for the orbifold Chow ring of weighted projective spaces},
journal = {Comm. Algebra 37 (2009) 503-514},
number = {arXiv.org;0709.4559v1},
year = {2009},
publisher = {Taylor and Francis},
abstract = {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.},
doi = {10.1080/00927870802248902},
url = {http://hdl.handle.net/1963/3589},
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}
}
@mastersthesis {2005,
title = {Orbifold Cohomology of ADE-singularities},
year = {2005},
school = {SISSA},
keywords = {Orbifolds},
url = {http://hdl.handle.net/1963/5298},
author = {Fabio Perroni}
}