On Self-Intersection Number of a Section on a Ruled Surface
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In this article, it was shown that a ruled surface which is birational to a surface obtained by successive elementary transformations from F is biregular to the surface obtained from F.Abstract:
Let E be a non-singular projective curve of genus g ≥ 0, P the projective line and let F be the surface E×P. Then it is well known that a ruled surface F* which is birational to F is biregular to a surface which is obtained by successive elementary transformations from F (for the notion of an elementary transformation, see [3]).read more
Citations
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Journal ArticleDOI
On the projective normality of complete linear series on an algebraic curve.
Mark Green,Robert Lazarsfeld +1 more
Journal ArticleDOI
Maximal Subbundles of Rank Two Vector Bundles on Curves.
H. Lange,M. S. Narasimhan +1 more
Book ChapterDOI
On the Canonical Ring of a Curve
Kapil H. Paranjape,S. Ramanan +1 more
TL;DR: For every semistable vector bundle W with integral μ, one may associate a subvariety D w of J g -1-μ as follows: D w = { ξ∈ J 9-1- μ : Γ(ξ ⊗W)≠ 0}. Indeed, if D w is a proper sub-variety, then one can actually associate an effective divisor algebraically equivalent to ( rkW ) θ of which Dw is the support as mentioned in this paper.
Journal ArticleDOI
On the Behavior of Extensions of Vector Bundles Under the Frobenius Map
TL;DR: In this article, the authors studied the behavior of the Frobenius map F*: H 1(X, E) → H 1 (X, F*E) for a vector bundle E.
References
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Journal ArticleDOI
On rational surfaces, II
TL;DR: In this paper, the authors introduce the notion of virtual linear systems on a non-singular projective surface and clarify the theories of infinitely near points, of divisors and of linear system with preassigned base conditions.