Alberto Canonaco — Page 2

arXiv2006

Twisted Fourier-Mukai functors

Due to a theorem by Orlov every exact fully faithful functor between the bounded derived categories of coherent sheaves on smooth projective varieties is of Fourier-Mukai type. We extend this result to the case of bounded derived categories of twisted coherent sheaves and at the same time we weaken the hypotheses on the functor. As an application we get a complete description of the exact functors between the abelian categories of twisted coherent sheaves on smooth projective varieties.

math.AG↗

arXiv2006

The Beilinson complex and canonical rings of irregular surfaces

In the first part of the paper Beilinson's theorem on the bounded derived category of coherent sheaves on P^n is extended to weighted projective spaces in a rather explicit form. To this purpose the usual category of coherent sheaves is replaced by a suitable category of graded sheaves, and a more general theory of graded schemes is developed. In the second part of the paper the weighted version of Beilinson's theorem is applied to prove a structure theorem for certain canonical projections of surfaces of general type into a 3-dimensional weighted projective space. This result (which generalizes to the weighted case a theorem by Catanese and Schreyer) is mainly interesting for irregular surfaces, and we illustrate it by studying a family of surfaces with p_g=q=2 and K^2=4, whose canonical rings are explicitly computed along the way.

math.AG↗