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1.
For a smooth irreducible complete algebraic curveC the “gaps” are the integersn such that every linear series of degreen has at least a base point. The Lüroth semigroup SC of a curveC is the subsemigroup ofN whose elements are not gaps. In this paper we deal with irreducible smooth curves of type (a, b) on a smooth quadricQ. The main result is an algorithm by which we can say if some integer λ∈N is a gap or is in SC. In the general case there are integers λ which are undecidable. For curves such as complete intersection, arithmetically
Cohen-Macaulay or Buchsbaum, we are able to describe explicitly “intervals” of gaps and “intervals” of integers which belong
to SC. For particular cases we can completely determine SC, by giving just the type of the curve (in particular the degree and the genus).
Work done with financial support of M.U.R.S.T. while the authors were members of G.N.S.A.G.A. of C.N.R. 相似文献
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Sam Payne 《Mathematische Zeitschrift》2006,253(2):421-431
We show that the dual of the cone of divisors on a complete -factorial toric variety X whose stable base loci have dimension less than k is generated by curves on small modifications of X that move in families sweeping out the birational transforms of k-dimensional subvarieties of X. We give an example showing that it does not suffice to consider curves on X itself.
Supported by a Graduate Research Fellowship from the NSF 相似文献
4.
Joseph Ross 《Journal of Pure and Applied Algebra》2011,215(11):2586-2599
For a smooth projective variety X of dimension n, on the product of Chow varieties Ca(X)×Cn−a−1(X) parameterizing pairs (A,B) of an a-cycle A and an (n−a−1)-cycle B in X, Barry Mazur raised the problem of constructing a Cartier divisor supported on the locus of pairs with A∩B≠0?. We introduce a new approach to this problem, and new techniques supporting this approach. 相似文献
5.
Let be a prime. We show that the space of weight one Eisenstein series defines an embedding into ${mathbb P}^{(p-3)/2}X_1(p)$ for the congruence group that is scheme-theoretically cut out by explicit quadratic equations. Received: 8 November 2000 / Published online: 17 August 2001 相似文献
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Marco Franciosi 《Advances in Mathematics》2004,186(2):317-333
Let C be a numerically connected curve lying on a smooth algebraic surface. We show that if is an ample invertible sheaf satisfying some technical numerical hypotheses then is normally generated. As a corollary we show that the sheaf ωC⊗2 on a numerically connected curve C of arithmetic genus pa?3 is normally generated if ωC is ample and does not exist a subcurve B⊂C such that pa(B)=1=B(C−B). 相似文献
8.
Let C1,···,Cd be Mumford curves defined over a finite extension of and let X=C1×···×Cd. We shall show the following: (1) The cycle map CH0(X)/n → H2d(X, μn⊗d) is injective for any non-zero integer n. (2) The kernel of the canonical map CH0(X)→Hom(Br(X),) (defined by the Brauer-Manin pairing) coincides with the maximal divisible subgroup in CH0(X). 相似文献
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Jean-Philippe Monnier 《manuscripta mathematica》2007,124(4):459-480
We bound the number of fixed points of an automorphism of a real curve in terms of the genus and the number of connected components
of the real part of the curve. Using this bound, we derive some consequences concerning the maximum order of an automorphism
and the maximum order of an abelian group of automorphisms of a real curve. We also bound the full group of automorphisms
of a real hyperelliptic curve.
Work supported by the European Community’s Human Potential Programme under contract HPRN-CT-2001-00271, RAAG. 相似文献
11.
Enric Nart 《Advances in Mathematics》2009,221(3):774-787
We find a closed formula for the number hyp(g) of hyperelliptic curves of genus g over a finite field k=Fq of odd characteristic. These numbers hyp(g) are expressed as a polynomial in q with integer coefficients that depend on g and the set of divisors of q−1 and q+1. As a by-product we obtain a closed formula for the number of self-dual curves of genus g. A hyperelliptic curve is defined to be self-dual if it is k-isomorphic to its own hyperelliptic twist. 相似文献
12.
Cícero F. Carvalho 《manuscripta mathematica》1999,98(2):155-163
We start this work by studying free linear systems on singular curves and related base point free linear systems on the non-singular
model. We apply these results to the study of pencils of small degree on non-singular curves. We also prove a “base point
free pencil trick” which holds for any (possibly) singular curve.
Received: 15 June 1998 相似文献
13.
C. Soulé 《Advances in Mathematics》2005,198(1):107-127
Atiyah and Hirzebruch gave examples of even degree torsion classes in the singular cohomology of a smooth complex projective manifold, which are not Poincaré dual to an algebraic cycle. We notice that the order of these classes must be small compared to the dimension of the manifold. However, building upon a construction of Kollár, one can provide such examples with arbitrary high prime order, the dimension being fixed. This method also provides examples of torsion algebraic cycles, which are non trivial in the Griffiths group, and lie in a arbitrary high level of the H. Saito filtration on Chow groups. 相似文献
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Chad Schoen 《Mathematische Zeitschrift》2006,252(1):11-17
An example is given in which specialization is not injective.
Partial support by the NSF (DMS-0200012) gratefully acknowledged. 相似文献
15.
Self-adjoint determinantal representations of real plane curves 总被引:3,自引:0,他引:3
Victor Vinnikov 《Mathematische Annalen》1993,296(1):453-479
Research supported by a Chaim Weizmann Fellowship, Weizmann Institute of Science, Rehovot, Israel. 相似文献
16.
Sandra Di Rocco 《Mathematische Zeitschrift》1999,231(1):169-188
The notion of a k-convex -support function for a toric variety is introduced. A criterion for a line bundle L to generate k-jets on X is given in terms of the k-convexity of the -support function . Equivalently L is proved to be k-jet ample if and only if the restriction to each invariant curve has degree at least k.
Received October 22, 1997; in final form January 12, 1998 相似文献
17.
Numerically positive line bundles on a complex projective smooth algebraic surfaceS are studied. In particular for any such line bundleL Pic(S) we prove the following facts: (i)g(L) 0 and (ii)L is ample ifg(L) 1,g standing for the arithmetic genus. Some applications are discussed. We also investigate numerically positive non-ample line bundlesL withg(L)=2. 相似文献
18.
Reza Akhtar 《Journal of Pure and Applied Algebra》2005,196(1):21-37
Let A be an abelian variety over a field k. We consider
CH0(A) as a ring under Pontryagin product and relate powers of the ideal
I⊆CH0(A) of degree zero elements to powers of the algebraic equivalence relation. We also consider a filtration
F0⊇F1⊇… on the Chow groups of varieties of the form
T×kA (defined using Pontryagin products on
A×kA considered as an A-scheme via projection on the first factor) and prove that
Fr coincides with the r-fold product
(F1)*r as adequate equivalence relations on the category of all such varieties. 相似文献
19.
The purpose of this paper is to construct non-trivial elements in the Abel–Jacobi kernels in any codimension by specializing correspondences with non-trivial Hodge-theoretical invariants at points with different transcendence degrees over a subfield in C. 相似文献
20.
We prove that certain integers n cannot occur as degrees of linear series without base points on the normalization of a plane
curve whose only singularities are a “small” number of nodes and ordinary cusps. As a consequence we compute the gonality
of such a curve.
Work done with financial support of M.U.R.S.T. while the authors were members of C.N.R. 相似文献