TY - JOUR
T1 - Pseudo-automorphisms of positive entropy on the blowups of products of projective spaces
Y1 - 2014
A1 - Fabio Perroni
A1 - Deqi Zhang
AB - 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.
PB - Springer
UR - http://urania.sissa.it/xmlui/handle/1963/34714
U1 - 34921
U2 - Mathematics
U4 - 1
ER -
TY - JOUR
T1 - Genus stabilization for moduli of curves with symmetries
Y1 - 2013
A1 - Fabrizio Catanese
A1 - Michael Lönne
A1 - Fabio Perroni
KW - group actions
KW - mapping class group
KW - Moduli space of curves
KW - Teichmüller space
AB - 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 $\\e$.
PB - SISSA
UR - http://hdl.handle.net/1963/6509
N1 - 21 pages, 2 figures
U1 - 6461
U2 - Mathematics
U4 - 1
U5 - MAT/03 GEOMETRIA
ER -
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 - Chen-Ruan cohomology of ADE singularities
JF - International Journal of Mathematics. Volume 18, Issue 9, October 2007, Pages 1009-1059
Y1 - 2007
A1 - Fabio Perroni
KW - Chen-Ruan cohomology, Ruan\'s conjecture, McKay correspondence
AB - 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.
PB - SISSA
UR - http://hdl.handle.net/1963/6502
N1 - 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)
U1 - 6447
U2 - Mathematics
U4 - 1
U5 - MAT/03 GEOMETRIA
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 - THES
T1 - Orbifold Cohomology of ADE-singularities
Y1 - 2005
A1 - Fabio Perroni
KW - Orbifolds
PB - SISSA
UR - http://hdl.handle.net/1963/5298
U1 - 5126
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -