41 research outputs found
Some Koszul Rings from Geometry
We give examples of Koszul rings that arise naturally in algebraic geometry.
In the first part, we prove a general result on Koszul property associated to
an ample line bundle on a projective variety. Specifically, we show how Koszul
property of multiples of a base point free ample line bundle depends on its
Castelnuovo-Mumford regularity. In the second part, we give examples of Koszul
rings that come from adjoint line bundles on irregular surfaces of general
type.Comment: 18 pages; reference added; some minor changes of notatio
Toroidalization of Locally Toroidal Morphisms from N-folds to Surfaces
The toroidalization conjecture of D. Abramovich, K. Karu, K. Matsuki, and J.
Wlodarczyk asks whether any given morphism of nonsingular varieties over an
algebraically closed field of characteristic zero can be modified into a
toroidal morphism. Following a suggestion by Dale Cutkosky, we define the
notion of \emph{locally toroidal} morphisms and ask whether any locally
toroidal morphism can be modified into a toroidal morphism. In this paper, we
answer the question in the affirmative when the morphism is between any
arbitrary variety and a surface.Comment: 22 pages. Final version (added an outline of the proof to the
introduction, fixed some errors of notation); to appear in J of Pure and
Applied Algebr
Single point Seshadri constants on rational surfaces
Motivated by a similar result of Dumnicki, K\"uronya, Maclean and Szemberg
under a slightly stronger hypothesis, we exhibit irrational single-point
Seshadri constants on a rational surface obtained by blowing up very
general points of , assuming only that all prime
divisors on of negative self-intersection are smooth rational curves
with . (This assumption is a consequence of the SHGH Conjecture, but it
is weaker than assuming the full conjecture.)Comment: 5 pages; minor changes since the original submission (additional
references, slightly re-written introduction and proofs); to appear in J.
Algebr