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 GĂ¶ttsche
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 -