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Let X be a hyperelliptic curve of arithmetic genus g and let f:XP1 be the hyperelliptic involution map of X. In this paper we study higher syzygies of linearly normal embeddings of X of degree d≤2g. Note that the minimal free resolution of X of degree ≥2g+1 is already completely known. Let A=fOP1(1), and let L be a very ample line bundle on X of degree d≤2g. For , we call the pair (m,d−2m)the factorization type ofL. Our main result is that the Hartshorne-Rao module and the graded Betti numbers of the linearly normal curve embedded by |L| are precisely determined by the factorization type of L.  相似文献   

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We obtain new examples and the complete list of the rational cuspidal plane curvesC with at least three cusps, one of which has multiplicitydegC-2. It occurs that these curves are projectively rigid. We also discuss the general problem of projective rigidity of rational cuspidal plane curves.  相似文献   

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In this paper we study defining equations and syzygies among them of projective bundles. We prove that for a given p≥0, if a vector bundle on a smooth complex projective variety is sufficiently ample, then the embedding given by the tautological line bundle satisfies property Np.  相似文献   

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For a 0-dimensional schemeX on a smooth quadricQ we define a special type of resolution of its ideal sheaf as a locally freeO Q. These resolutions allow to find, for schemes which are generic inQ, the minimal free resolution ofX as a subscheme of ℙ3. For almost all such schemes the graded Betti numbers in ℙ3 depend only on the Hilbert function ofX in ℙ3. Work done with financial support of M.U.R.S.T., while the authors were members of C.N.R.  相似文献   

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A tetrahedral curve is a (usually nonreduced) curve in P3 defined by an unmixed, height two ideal generated by monomials. We characterize when these curves are arithmetically Cohen-Macaulay by associating a graph with each curve and, using results from combinatorial commutative algebra and Alexander duality, relating the structure of the complementary graph to the Cohen-Macaulay property.  相似文献   

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The ideal of a Segre variety Pn1×?×Pnt?P(n1+1)?(nt+1)−1 is generated by the 2-minors of a generic hypermatrix of indeterminates (see [H.T. Hà, Box-shaped matrices and the defining ideal of certain blowup surface, J. Pure Appl. Algebra 167 (2-3) (2002) 203-224. MR1874542 (2002h:13020)] and [R. Grone, Decomposable tensors as a quadratic variety, Proc. Amer. Math. 43 (2) (1977) 227-230. MR0472853 (57 #12542)]). We extend this result to the case of Segre-Veronese varieties. The main tool is the concept of “weak generic hypermatrix” which allows us to treat also the case of projection of Veronese surfaces from a set of general points and of Veronese varieties from a Cohen-Macaulay subvariety of codimension 2.  相似文献   

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In this note we describe the minimal resolution of the ideal If, the saturation of the Jacobian ideal of a nearly free plane curve C:f=0. In particular, it follows that this ideal If can be generated by at most 4 polynomials. Related general results by Hassanzadeh and Simis on the saturation of codimension 2 ideals are discussed in detail. Some applications to rational cuspidal plane curves and to line arrangements are also given.  相似文献   

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Let X be a smooth projective surface defined over , and let L be a line bundle over X such that for every complete curve Y contained in X. A question of Keel asks whether L is ample. If X is a P1-bundle over a curve, we prove that this question has an affirmative answer.  相似文献   

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C. Ciliberto  S. Greco 《代数通讯》2013,41(12):5891-5913
We construct families of normal surface singularities with the following property: given any fiat projective connected family VB of smooth, irreducible, minimal algebraic surfaces, the general singularity in one of our families cannot occur, analytically, on any algebraic surfaces which is Irrationally equivalent to a surface in VB. In particular this holds for VB consisting of a single rational surface, thus answering negatively to a long standing problem posed by F. Enriques. In order to prove the above mentioned results, wo develop a general, though elementary, method, based on the consideration of suitable correspondences, for comparing a given family of minimal surfaces with a family of surface singularities. Specifically the method in question gives us the possibility of comparing the parameters on which the two families depend, thus leading to the aforementioned results.  相似文献   

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Let X be a non-degenerate, not necessarily linearly normal projective variety in . Recently the generalization of property N p to non-linearly normal projective varieties have been considered and its algebraic and geometric properties are studied extensively. One of the generalizations is the property N d,p for the saturated ideal I X (Eisenbud et al. in Compos Math 141: 1460–1478, 2005) and the other is the property for the graded module of the twisted global sections of (Kwak and Park in J Reine Angew Math 582: 87–105, 2005). In this paper, we are interested in the algebraic and geometric meaning of properties for every p ≥ 0 and the syzygetic behaviors of isomorphic projections and hyperplane sections of a given variety with property . Youngook Choi and Sijong Kwak were supported in part by KRF (grant No. 2005-070-C00005).  相似文献   

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In [CH3], Caporaso and Harris derive recursive formulas counting nodal plane curves of degree d and geometric genus g in the plane (through the appropriate number of fixed general points). We rephrase their arguments in the language of maps, and extend them to other rational surfaces, and other specified intersections with a divisor. As applications, (i) we count irreducible curves on Hirzebruch surfaces in a fixed divisor class and of fixed geometric genus, (ii) we compute the higher-genus Gromov–Witten invariants of (or equivalently, counting curves of any genus and divisor class on) del Pezzo surfaces of degree at least 3. In the case of the cubic surface in (ii), we first use a result of Graber to enumeratively interpret higher-genus Gromov–Witten invariants of certain K-nef surfaces, and then apply this to a degeneration of a cubic surface. Received: 30 June 1999 / Revised version: 1 January 2000  相似文献   

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In this note we develop some of the properties of separators of points in a multiprojective space. In particular, we prove multigraded analogs of results of Geramita, Maroscia, and Roberts relating the Hilbert function of and via the degree of a separator, and Abrescia, Bazzotti, and Marino relating the degree of a separator to shifts in the minimal multigraded free resolution of the ideal of points.  相似文献   

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It is a longstanding problem in Algebraic Geometry to determine whether the syzygy bundle Ed1,…,dn on PN defined as the kernel of a general epimorphism
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Supported, in part, by the Natural Sciences and Engineering Research Council of Canada  相似文献   

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In this paper it is shown that the gonality of curves on an elliptic ruled surface is twice the degree of the restriction of the bundle map and the Clifford index of such curves is computed by pencils of minimal degree, under certain numerical conditions. It is also proved that any pencil computing the gonality and the Clifford index of curves is composed with the restriction of the bundle map under some stronger conditions. On the other hand, we found some counterexample to the constancy of gonality and Clifford index in a linear system.Received: 2 December 2003  相似文献   

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