%0 Journal Article
%J Communications in Algebra. Volume 41, Issue 6, May 2013, Pages 2346-2386
%D 2013
%T Expanded degenerations and pairs
%A Dan Abramovich
%A Charles Cadman
%A Barbara Fantechi
%A Jonathan Wise
%K Expanded pairs
%X 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.
%B Communications in Algebra. Volume 41, Issue 6, May 2013, Pages 2346-2386
%I Taylor and Francis
%G en
%U http://hdl.handle.net/1963/7383
%1 7431
%2 Mathematics
%4 1
%# MAT/05 ANALISI MATEMATICA
%$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-18T09:55:33Z
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%R 10.1080/00927872.2012.658589
%0 Journal Article
%J Geom. Topol. 14 (2010) 83-115
%D 2010
%T Riemann-Roch theorems and elliptic genus for virtually smooth schemes
%A Barbara Fantechi
%A Lothar Göttsche
%X 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.
%B Geom. Topol. 14 (2010) 83-115
%I Mathematical Sciences Publishers
%G en_US
%U http://hdl.handle.net/1963/3888
%1 821
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-23T07:35:11Z\\nNo. of bitstreams: 1\\n0706.0988v1.pdf: 396801 bytes, checksum: 640403457a0a02c4166b8c684d8af419 (MD5)
%R 10.2140/gt.2010.14.83
%0 Journal Article
%J Algebra Number Theory 2 (2008) 313-345
%D 2008
%T Symmetric obstruction theories and Hilbert schemes of points on threefolds
%A Kai Behrend
%A Barbara Fantechi
%X 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.
%B Algebra Number Theory 2 (2008) 313-345
%G en_US
%U http://hdl.handle.net/1963/2709
%1 1392
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-22T08:20:28Z\\nNo. of bitstreams: 1\\n0512556v1.pdf: 377619 bytes, checksum: ba4796d5d4103e23a359d4fe4d01ca2f (MD5)
%0 Report
%D 2007
%T Smooth toric DM stacks
%A Barbara Fantechi
%A Etienne Mann
%A Fabio Nironi
%X 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.
%G en_US
%U http://hdl.handle.net/1963/2120
%1 2123
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T06:41:10Z\\nNo. of bitstreams: 1\\ntoricarxiv.pdf: 426672 bytes, checksum: e73e63b89023046b5d53b7f7f6c2e580 (MD5)