Gonality, Clifford index and multisecants
英文摘要:
We show, among other things, that in most cases the gonality of a subcanonical curve in projective-three space is computable by multisecants.
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Ph. Ellia, D. Franco
We show, among other things, that in most cases the gonality of a subcanonical curve in projective-three space is computable by multisecants.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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In this paper we review the notions of gonality and Clifford index of an abstract curve. For a curve embedded in a projective space, we investigate the connection between the \ci of the curve and the \gc al properties of its \emb. In particular if $C$ is a curve of degree $d$ in $¶^3$, and if $L$ is a multisecant of maximum order $k$, then the pencil of planes through $L$ cuts out a $g^1_{d-k}$ on $C$. If the gonality of $C$ is equal to $d-k$ we say the gonality of $C$ can be computed by multisecants. We discuss the question whether the \go of every smooth ACM curve in $¶^3$ can be computed by…
We show that every possible value for the Clifford index and gonality of a curve of a given genus on a $K3$ surface occurs.
We determine the gonality and the Clifford index for curves on a compact smooth toric surface. Moreover, it is shown that their gonality are computed by pencils on the ambient surface. From the geometrical view point, this means that the gonality can be read off from the lattice polygon associated to the curve.
We compute the Clifford index of all curves on a K3 surface with Picard group isomorphic to U(m).
Let C be an ACM (projectively normal) nondegenerate smooth curve in projective 3-space, and suppose C is general in its Hilbert scheme - this is irreducible once the postulation is fixed. Answering a question posed by Peskine, we show the gonality of C is d-l, where d is the degree of the curve, and l is the maximum order of a multisecant line of C. Furthermore l=4 except for two series of cases, in which the postulation of C forces every surface of minimum degree containing C to contain a line as well. We compute the value of l in terms of the postulation of C in these exceptional cases. We a…
We extend the results of Pareschi on the constancy of the gonality and Clifford index of smooth curves in a complete linear system on Del Pezzo surfaces of degrees $\geq 2$ to the case of Del Pezzo surfaces of degree 1, where we explicitly classify the cases where the gonality and Clifford index are not constant. We also classify all cases of exceptional curves on Del Pezzo surfaces, which turn out to be the smooth plane curves and some other cases with Clifford dimension 3. Moreover, the property of being exceptional holds for all curves in the complete linear system. Furthermore, we relate t…
Green's conjecture is proved for smooth curves C lying on a rational surface S with an anticanonical pencil, under some mild hypotheses on the line bundle L defined by C. Constancy of Clifford dimension, Clifford index and gonality of curves in the linear system |L| is also obtained.
Second gonality of smooth aCM curves on quartic surfaces in $\mathbb{P}^3$
研究光滑aCM曲线在$\mathbb{P}^3$中四次曲面的第二亏约数,通过曲线上的网计算其亏约数,确定最小的线性系参数。
We generalize, for integral curves, a celebrated result of Max Noether on global sections of the n-dualizing sheaf of a smooth nonhyperelliptic curve. This is our main result. We also obtain an embedding of a non-Gorenstein curve in a way that we can express the dimensions of the components of the ideal in terms of the main invariants of the curve. Afterwards we focus on gonality, Clifford index and Koszul cohomology of non-Gorenstein curves by allowing torsion free sheaves of rank 1 in their definitions. We find an upper bound for the gonality, which agrees with Brill-Noether's one for a rati…
The main purpose in this paper is to study the gonality, the Clifford index and the Clifford dimension on linearly equivalent smooth curves on Enriques surfaces. The method is similar to techniques of M.Green $\&$ R.Lazarsfeld and G.Pareschi.
It has been a long-standing problem to find an adequate definition of a Clifford index for higher rank vector bundles on curves, which should capture the complexity of the curve in its moduli space. An interesting proposal in rank 2 has been put forward by Mercat, who conjectured that the second Clifford index of a curve should be equal to its classical Clifford index, defined in terms of gonality. Using moduli of sheaves on generic K3 surfaces, we prove Mercat's conjecture for generic curves of every genus. Furthermore, for odd g we identify an effective divisor in the moduli space M_g along …
Syzygies of canonical ribbons on higher genus curves
研究高亏格曲线上典范ribbon的合冲,证明一般ribbon的两种Clifford指标相等,指出分裂ribbon的指标相等与亏格猜想、Green猜想相关,并将其简化为辅助合冲模Koszul上同调群的消失问题。
A remark on du Val linear systems
本文证明了在 Halphen 曲面上的 du Val 线性系统中,光滑曲线的 Clifford 指数为常数,并在相关情形下确定了其度数由 Weierstrass 线性系实现。
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