M. A. Barja, L. Stoppino
Let f :S\to B be a non locally trivial fibred surface. We prove a lower bound for the slope of f depending increasingly from the relative irregularity of f and the Clifford index of the general fibres.
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。
继续探索
We prove new slope inequalities for relatively minimal fibred surfaces, showing an influence of the relative irregularity, of the unitary rank and of the Clifford index on the slope. The argument uses Xiao's method and a new Clifford-type inequality for subcanonical systems on non-hyperelliptic curves.
In this paper we present a generalisation of a theorem due to Cornalba and Harris, which is an application of Geometric Invariant Theory to the study of invariants of fibrations. In particular, our generalisation makes it possible to treat the problem of bounding the invariants of general fibred surfaces. As a first application, we give a new proof of the slope inequality and of a bound for the invariants associated to double cover fibrations.
Given a relatively minimal non locally trivial fibred surface f: S->B, the slope of the fibration is a numerical invariant associated to the fibration. In this paper we explore how properties of the general fibre of $f$ and global properties of S influence on the lower bound of the slope. First of all we obtain lower bounds of the slope when the general fibre is a double cover. We also obtain a lower bound depending as an increasing function on the relative irregularity of the fibration, extending previous results of Xiao. We construct several families of examples to check the assimptotical sh…
Let $f:\,S \to B$ be a locally non-trivial relatively minimal fibration of genus $g\geq 2$ with relative irregularity $q_f$. It was conjectured by Barja and Stoppino that the slope $λ_f\geq \frac{4(g-1)}{g-q_f}$. We prove the conjecture when $q_f$ is small with respect to $g$; we also construct counterexamples when $g$ is odd and $q_f=(g+1)/2$.
Slopes of trigonal fibred surfaces and of higher dimensional fibrations
本文推广Cornalba-Harris方法，在GIT半稳定条件下给出高维纤维化斜率下界，并证明偶数亏格三角纤维化斜率的锐利下界，从而证实Harris-Stankova猜想。
We study from a geographical point of view fibrations of threefolds over smooth curves, such that the general fibre is of general type. We prove the non-negativity of certain relative invariants under general hypotheses and give lower bounds for the self-interssection of the relative canonical divisor of the fibration, depending on other relative invariants. We also study the influence of the relative irregularity on these bounds. A more detailed study of the lowest cases of the bounds is given.
Let f: X->B be a fibred surface of genus g whose general fibre is a double cover of a smooth curve of genus gamma. We show that, for g > 4gamma+1, the number 4(g-1)/(g-gamma) is a sharp lower bound for the slope of f, proving a conjecture of Barja. Moreover, we give a characterisation of the fibred surfaces that reach the bound. In the case g = 4gamma+1 we obtain the same sharp bound under the assumption that the involutions on the general fibres glue to a global involution on X.
We study and obtain Slope inequalities for fibred irregular varieties of non-maximal Albanese dimension. We give a comparison theorem between Clifford-Severi and Slope inequalities for this type of fibrations. We also obtain a set of Slope inequalities considering the geometry of the Albanese map and the associated eventual maps.
Locally non-trivial fibred surfaces with maximal unitary rank
该文研究具有最大酉秩$u_f=g-1$的局部非平凡纤维化曲面，证明强斜率不等式，结合三角曲线结果给出$g=6$、$u_f=5$情形的新约束，包括曲面指数严格为正及相对典范除子类的强限制。
K. Konno proved a slope equality for fibred surfaces with fibres of odd genus and general fibre of maximal gonality. More precisely he found a relation between the invariants of the fibration and certain weights of special fibres (called the Horikawa numbers). We give an alternative and more geometric proof in the case of a genus 5 fibration, under generality assumptions. In our setting we are able to prove that the fibre with positive Horikawa numbers are precisely the trigonal ones, we compute their weights explicitly and thus we exhibit explicit examples of regular surfaces with assigned in…
Fibred surfaces and their unitary rank
本文研究亏格至少为2的复纤维化曲面的酉秩，证明多个新斜率不等式，并由此得到非等平凡纤维化酉秩的Xiao型上界及Coleman-Oort猜想方向的新约束。
We strengthen a conjecture by the author. This conjecture is a Bogomolov-Gieseker type inequality involving the third Chern character of mixed tilt-stable complexes on fibred threefolds. We extend it from complexes of mixed tilt-slope zero to arbitrary relative tilt-slope. We show that this stronger conjecture implies the support property of Bridgeland stability conditions, and the existence of explicit stability conditions. We prove our conjecture for ruled threefolds, hence improving a previous result by the author.
Let f:S ->B be a relatively minimal fibred surface. In this note we give a partial affirmative answer to a conjecture of Xiao, proving that the direct image of the relative dualizing sheaf of $f$ is ample when the slope of the fibration is less than 4, if the general fibre of $f$ is non-hyperelliptic or the genus of the fibre or of the base curve is low.
Being inspired by Ross' construction of unstable products of certain smooth curves, we show that the product $C\times C$ of every smooth curve $C$ of genus at least 2 is not slope semistable with respect to certain polarisations. Besides, we produce examples of Kodaira-fibred surfaces of nonzero signature, which are not slope semistable with respect to some polarisations, and so they admit Kähler classes that do not contain any constant scalar curvature Kähler metrics.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。