Very Ampleness and Higher Syzygies for Algebraic Surfaces and Calabi-Yau Threefolds

Details Very Ampleness and Higher Syzygies for Algebraic Surfaces and Calabi-Yau Threefolds Very Ampleness and Higher Syzygies for Algebraic Surfaces and Calabi-Yau Threefolds

1997-03-28

arxiv.org/abs/alg-geom/9703036v3

Mathematics

Algebraic Geometry

AMS TeX, 44 pages. The manuscript has been rewritten and now consists of two parts. First part is on syzygies of surfaces and

Scientific paper

This work consists of two parts. In the first part we develop new techniques to compute Koszul cohomology groups for several classes of varieties. As applications we prove results on projective normality and syzygies for algebraic surfaces. From more general results we obtain in particular the following: a) Mukai's conjecture (and stronger variants of it) regarding projective normality and normal presentation for surfaces with Kodaira dimension 0, and uniform bounds for higher syzygies associated to adjoint linear series, b) effective bounds along the lines of Mukai's conjecture regarding projective normality and normal presentation for surfaces of positive Kodaira dimension, and, c) results on projective normality for pluricanonical models of surfaces of general type (recovering and strengthening results by Ciliberto) and generalizations of them to higher syzygies. In the second part we prove results on very ampleness, projective normality and higher syzygies for both singular and smooth Calabi-Yau threefolds. The general results that we prove are analogues of the results of St. Donat for K3 surfaces. From these general results we obtain bounds very close to Fujita's conjecture regarding very ampleness of powers of an ample line bundle A (for instance, if A^3 is greater than 1, our bound is one short of Fujita's). We generalize our results on very ampleness and projective normality to higher syzygies.

Affiliated with

Also associated with

No associations

Rating

Very Ampleness and Higher Syzygies for Algebraic Surfaces and Calabi-Yau Threefolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Very Ampleness and Higher Syzygies for Algebraic Surfaces and Calabi-Yau Threefolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Very Ampleness and Higher Syzygies for Algebraic Surfaces and Calabi-Yau Threefolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-28048