The Beilinson Complex and Canonical Rings of Irregular Surfaces

Released on by Alberto Canonaco
preview-18

  • The Beilinson Complex and Canonical Rings of Irregular Surfaces Book Detail

  • Author : Alberto Canonaco
  • Release Date : 2006
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 114
  • ISBN 13 : 0821841939
  • File Size : 45,45 MB
DOWNLOAD BOOK

The Beilinson Complex and Canonical Rings of Irregular Surfaces by Alberto Canonaco PDF Summary

Book Description: An important theorem by Beilinson describes the bounded derived category of coherent sheaves on $\mathbb{P n$, yielding in particular a resolution of every coherent sheaf on $\mathbb{P n$ in terms of the vector bundles $\Omega {\mathbb{P n j(j)$ for $0\le j\le n$. This theorem is here extended to weighted projective spaces. To this purpose we consider, instead of the usual category of coherent sheaves on $\mathbb{P ({\rm w )$ (the weighted projective space of weights $\rm w=({\rm w 0,\dots,{\rm w n)$), a suitable category of graded coherent sheaves (the two categories are equivalent if and only if ${\rm w 0=\cdots={\rm w n=1$, i.e. $\mathbb{P ({\rm w )= \mathbb{P n$), obtained by endowing $\mathbb{P ({\rm w )$ with a natural graded structure sheaf. The resulting graded ringed space $\overline{\mathbb{P ({\rm w )$ is an example of graded scheme (in chapter 1 graded schemes are defined and studied in some greater generality than is needed in the rest of the work). Then in chapter 2 we prove This weighted version of Beilinson's theorem is then applied in chapter 3 to prove a structure theorem for good birational weighted canonical projections of surfaces of general type (i.e., for morphisms, which are birational onto the image, from a minimal surface of general type $S$ into a $3$-dimensional $\mathbb{P ({\rm w )$, induced by $4$ sections $\sigma i\in H0(S,\mathcal{O S({\rm w iK S))$). This is a generalization of a theorem by Catanese and Schreyer (who treated the case of projections into $\mathbb{P 3$), and is mainly interesting for irregular surfaces, since in the regular case a similar but simpler result (due to Catanese) was already known. The theorem essentially states that giving a good birational weighted canonical projection is equivalent to giving a symmetric morphism of (graded) vector bundles on $\overline{\mathbb{P ({\rm w )$, satisfying some suitable conditions. Such a morphism is then explicitly determined in chapter 4 for a family of surfaces with numerical invariant

Disclaimer: www.yourbookbest.com does not own The Beilinson Complex and Canonical Rings of Irregular Surfaces books pdf, neither created or scanned. We just provide the link that is already available on the internet, public domain and in Google Drive. If any way it violates the law or has any issues, then kindly mail us via contact us page to request the removal of the link.

Finite Sections of Band-Dominated Operators

Finite Sections of Band-Dominated Operators

File Size : 17,17 MB
Total View : 5541 Views
DOWNLOAD

The goal of this text is to review recent advances and to present new results in the numerical analysis of the finite sections method for general band and band-

KAM Stability and Celestial Mechanics

KAM Stability and Celestial Mechanics

File Size : 71,71 MB
Total View : 4783 Views
DOWNLOAD

KAM theory is a powerful tool apt to prove perpetual stability in Hamiltonian systems, which are a perturbation of integrable ones. The smallness requirements f