This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Later, Stoppino [ 31 ] found a way to treat non-semi-stable fibrations using the idea of Cornalba—Harris [ 3 ]. It is not clear, at least to the author, that whether the aforementioned stability methods could give rise to a slope inequality over surfaces other than curves.

The author was asked by Professor Xiaotao Sun about a proof of 1. Arbarello, E.

### Stability Conditions and Positivity of Invariants of Fibrations

Barth, W. A Series of Modern Surveys in Mathematics], vol. Cornalba, M.

Cheatcc ps4Chen, K. Conrad, B. Lecture Notes in Mathematics, vol. Springer, Berlin Google Scholar. Cossart, V. Reduction to local uniformization on Artin-Schreier and purely inseparable coverings. Algebra 3— Algebra 7— Fujita, T. Grothendieck, A. Huybrechts, D.

Paintball sniperAspects of Mathematics, E Harris, J.Slope inequalities are given for fibred rational surfaces according as the Clifford index of a general fibre. For fibred rational surfaces of Clifford index two, the Mordell-Weil lattices of maximal ranks are completely determined. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve.

## Fibred rational surfaces with extremal Mordell-Weil lattices

Arbarello, E. Beauville, A. France— Google Scholar. Barja, M. AMS— Coppens, M. Compositio Math. Notes in Math. Green, M.

**Graphing Linear Inequalities 3 Examples**

Hartshorne, R. IHES 36— Iitaka, S. Saitama Math. Kitagawa, S. Japan 57— Miguel A. Barja More by Miguel A. Barja Search this author in:.

Full-text: Access denied no subscription detected We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text. We give a sharp lower bound for the self-intersection of a nef line bundle L on an irregular variety X in terms of its continuous global sections and the Albanese dimension of Xwhich we call the generalized Clifford—Severi inequality.

We also extend the result to nef vector bundles and give a slope inequality for fibered irregular varieties. Source Duke Math. Zentralblatt MATH identifier Keywords Severi inequality irregular variety nef line bundle continuous system.

Barja, Miguel A.

Generalized Clifford—Severi inequality and the volume of irregular varieties. Duke Math. More by Miguel A. Read more about accessing full-text Buy article. Abstract Article info and citation First page References Abstract We give a sharp lower bound for the self-intersection of a nef line bundle L on an irregular variety X in terms of its continuous global sections and the Albanese dimension of Xwhich we call the generalized Clifford—Severi inequality.

Article information Source Duke Math. Export citation. Export Cancel. References [1] M.

Hiikkaa jechoota macaafa qulqulluuBarja, M. Lahoz, J. Naranjo, and G. Pareschi, On the bicanonical map of irregular varietiesJ. Algebraic Geom. You have access to this content.

X99 a b6 codeYou have partial access to this content. You do not have access to this content. More like this.Algebraic and Complex Geometry pp Cite as. We study three methods that prove the positivity of a natural numerical invariant associated to 1-parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a natural connection between them, related to a yet another stability condition, the linear stability.

Finally we make some speculations and prove new results in higher dimension. Skip to main content. This service is more advanced with JavaScript available. Advertisement Hide. Stability Conditions and Positivity of Invariants of Fibrations.

Authors Authors and affiliations M. Barja L. Conference paper First Online: 23 July This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Alper, M. Fedorchuk, D. Smyth, Finite Hilbert stability of bi canonical curves.

Arbarello, M.

Bhojpuri dj 2020Cornalba, P. Griffiths, J. Harris, Geometry of Algebraic Curves. Grundlehren Der Mathematischen Wissenschaften, vol. II Springer, New York,p. Ashikaga, K. Konno, Global and local properties of pencils of algebraic curves, in Algebraic GeometryAzumino. Advanced Studies in Pure Mathematics, vol.

Barja, Generalized clifford-Severi inequality preprint. AG] Google Scholar. Barja, On the slope of fibred threefolds. Barja, L. Stoppino, Linear stability of projected canonical curves, with applications to the slope of fibred surfaces. Stoppino, Slopes of trigonal fibred surfaces and of higher dimensional fibrations.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. Source Osaka J. Zentralblatt MATH identifier Stoppino, Lidia.

Slope inequalities for fibred surfaces via GIT. Osaka J. Abstract Article info and citation First page References Abstract 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. Article information Source Osaka J. Export citation.

Export Cancel. References E. Arbarello, M. Cornalba, P. Griffiths and J. Harris: Geometry of algebraic curvesVol. II, in preparation. Ashikaga and K. Konno: Global and local properties of pencils of algebraic curves ; in Algebraic geometryAzumino HotakaAdv. Japan, Tokyo, You have access to this content.Albano and G. Pirola, Dihedral monodromy and Xiao fibrations, Ann. Pura App. Barja and L. Stoppino, Linear stability of projected canonical curves with applications to the slope of fibred surfaces, J.

Japan 60no. Cai, Irregularity of certain algebraic fiber spaces, Manuscripta Math. Collino and G.

Franceno. Japan 30no. Japan Acad. A Math. Konno, Clifford index and the slope of fibered surfaces, J. Algebraic Geom. Lu and K. Zuo, On the slope of hyperelliptic fibrations with positive relative irregularity, Trans. Pirola, Curves on generic Kummer varieties, Duke Math. Pirola, On a conjecture of Xiao, J.

Pirola and F. Zucconi, Variations of the Albanese morphisms, J. Serrano, Isotrivial fibred surfaces, Ann. Pura Appl. Xiao, Fibered algebraic surfaces with low slope, Math. Xiao, Irregularity of surfaces with a linear pencil, Duke Math.Fibered varieties over curves with low slope and sharp bounds in dimension three. Algebraic Geom. Abstract: In this paper, we first construct varieties of any dimension fibered over curves with low slopes.

These examples violate the conjectural slope inequality of Barja and Stoppino [Springer Proc. Led by their conjecture, we focus on finding the lowest possible slope when. Based on a characteristic method, we prove that the sharp lower bound of the slope of fibered -folds over curves isand it occurs only when the general fiber is a -surface.

Otherwise, the sharp lower bound is. We also obtain a Cornalba-Harris-Xiao-type slope inequality for families of surfaces of general type over curves, and it is sharper than all known results with no extra assumptions. As an application of the slope bound, we deduce a sharp Noether-Severi-type inequality that for an irregular minimal -fold of general type not having a -surface Albanese fibration.

It answers a question in [Canad. References [Enhancements On Off] What's this? Most recent issue All issues Recently published articles. BarjaLower bounds of the slope of fibred threefoldsInternat. Barja and Lidia Stoppino, Positivity properties of relative complete intersectionsarXiv Barja and L.

### Canonical class inequality for fibred spaces

StoppinoStability conditions and positivity of invariants of fibrationsAlgebraic and complex geometry, Springer Proc. IMRN 4— BombieriCanonical models of surfaces of general typeInst. MR [10] Jungkai A. Japan 56no. HaconOn the geography of Gorenstein minimal 3-folds of general typeAsian J. Franceno. With an appendix by A. Japan 44no. Pure Math.

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