TY - JOUR
T1 - Expanded degenerations and pairs
JF - Communications in Algebra. Volume 41, Issue 6, May 2013, Pages 2346-2386
Y1 - 2013
A1 - Dan Abramovich
A1 - Charles Cadman
A1 - Barbara Fantechi
A1 - Jonathan Wise
KW - Expanded pairs
AB - Since Jun Li's original definition, several other definitions of expanded pairs and expanded degenerations have appeared in the literature. We explain how these definitions are related and introduce several new variants and perspectives. Among these are the twisted expansions used by Abramovich and Fantechi as a basis for orbifold techniques in degeneation formulas.
PB - Taylor and Francis
UR - http://hdl.handle.net/1963/7383
N1 - This article is composed of 41 pages and is recorded in PDF format
U1 - 7431
U2 - Mathematics
U4 - 1
U5 - MAT/05 ANALISI MATEMATICA
ER -
TY - JOUR
T1 - Riemann-Roch theorems and elliptic genus for virtually smooth schemes
JF - Geom. Topol. 14 (2010) 83-115
Y1 - 2010
A1 - Barbara Fantechi
A1 - Lothar Göttsche
AB - For a proper scheme X with a fixed 1-perfect obstruction theory, we define virtual versions of holomorphic Euler characteristic, chi y-genus, and elliptic genus; they are deformation invariant, and extend the usual definition in the smooth case. We prove virtual versions of the Grothendieck-Riemann-Roch and Hirzebruch-Riemann-Roch theorems. We show that the virtual chi y-genus is a polynomial, and use this to define a virtual topological Euler characteristic. We prove that the virtual elliptic genus satisfies a Jacobi modularity property; we state and prove a localization theorem in the toric equivariant case. We show how some of our results apply to moduli spaces of stable sheaves.
PB - Mathematical Sciences Publishers
UR - http://hdl.handle.net/1963/3888
U1 - 821
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Symmetric obstruction theories and Hilbert schemes of points on threefolds
JF - Algebra Number Theory 2 (2008) 313-345
Y1 - 2008
A1 - Kai Behrend
A1 - Barbara Fantechi
AB - In an earlier paper by one of us (Behrend), Donaldson-Thomas type invariants were expressed as certain weighted Euler characteristics of the moduli space. The Euler characteristic is weighted by a certain canonical\\nZ-valued constructible function on the moduli space. This constructible function associates to\\nany point of the moduli space a certain invariant of the singularity of the space at the point. Here we evaluate this invariant for the case of a singularity that is an isolated point of a C∗-action and that admits a symmetric obstruction theory compatible with the C∗-action. The answer is (-1)d, where d\\nis the dimension of the Zariski tangent space. We use this result to prove that for any threefold, proper or not, the weighted Euler characteristic of the Hilbert scheme of n points on the threefold is, up to sign, equal to the usual Euler characteristic. For the case of a projective Calabi-Yau threefold, we deduce that the Donaldson-Thomas invariant of the Hilbert scheme of n points is, up to sign, equal to the Euler characteristic. This proves a conjecture of Maulik, Nekrasov, Okounkov and Pandharipande.
UR - http://hdl.handle.net/1963/2709
U1 - 1392
U2 - Mathematics
U3 - Mathematical Physics
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 -