Coherent Sheaves Superconnections and Riemann-Roch-Grothendieck

<div>This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology and the proof of a corresponding Riemann-Roch-Grothendieck  theorem.  One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections.  Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis by combining local index theory with the hypoelliptic Laplacian.</div><div><br></div><i>Coherent Sheaves Superconnections and Riemann-Roch-Grothendieck</i> is an important contribution to both the geometric and analytic study of complex manifolds and as such it will be a valuable resource formany researchers in geometry analysis and mathematical physics. <div><br></div>