@article {2010,
	title = {Riemann-Roch theorems and elliptic genus for virtually smooth schemes},
	journal = {Geom. Topol. 14 (2010) 83-115},
	number = {arXiv.org;0706.0988v1},
	year = {2010},
	publisher = {Mathematical Sciences Publishers},
	abstract = {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.},
	doi = {10.2140/gt.2010.14.83},
	url = {http://hdl.handle.net/1963/3888},
	author = {Barbara Fantechi and Lothar G{\"o}ttsche}
}
