Meromorphic singular foliations on complex projective surfaces

1996 ◽  
Vol 14 (3) ◽  
pp. 257-261
Author(s):  
Edoardo Ballico
Keyword(s):  
Singular Foliations ◽  
Complex Projective ◽  
Projective Surfaces

scholarly journals TRANSVERSELY PROJECTIVE FOLIATIONS ON SURFACES: EXISTENCE OF MINIMAL FORM AND PRESCRIPTION OF MONODROMY

2007 ◽  
Vol 18 (06) ◽  
pp. 723-747 ◽  
Author(s):  
FRANK LORAY ◽  
JORGE VITÓRIO PEREIRA
Keyword(s):  
Ambient Space ◽  
Two Dimensional ◽  
Complex Manifolds ◽  
Projective Structures ◽  
Singular Foliations ◽  
Minimal Form ◽  
Natural Way ◽  
Projective Surfaces

We introduce a notion of minimal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this minimal form exists and is unique when ambient space is two-dimensional. From this result, one obtains a natural way to produce invariants for transversely projective foliations on surfaces. Our second main result says that on projective surfaces one can construct singular transversely projective foliations with prescribed monodromy.

Complex projective surfaces and infinite groups

1998 ◽  
Vol 8 (2) ◽  
pp. 243-272 ◽  
Author(s):  
F. Bogomolov ◽  
L. Katzarkov
Keyword(s):  
Infinite Groups ◽  
Complex Projective ◽  
Projective Surfaces

scholarly journals Weyl and Zariski chambers on projective surfaces

2020 ◽  
Vol 32 (4) ◽  
pp. 1027-1037
Author(s):  
Krishna Hanumanthu ◽  
Nabanita Ray
Keyword(s):  
K3 Surfaces ◽  
Weyl Chamber ◽  
Projective Surface ◽  
Complex Projective Surface ◽  
Complex Projective ◽  
Projective Surfaces

AbstractLet X be a nonsingular complex projective surface. The Weyl and Zariski chambers give two interesting decompositions of the big cone of X. Following the ideas of [T. Bauer and M. Funke, Weyl and Zariski chambers on K3 surfaces, Forum Math. 24 2012, 3, 609–625] and [S. A. Rams and T. Szemberg, When are Zariski chambers numerically determined?, Forum Math. 28 2016, 6, 1159–1166], we study these two decompositions and determine when a Weyl chamber is contained in the interior of a Zariski chamber and vice versa. We also determine when a Weyl chamber can intersect non-trivially with a Zariski chamber.

On complex projective surfaces with trigonal hyperplane sections

1989 ◽  
Vol 65 (1) ◽  
pp. 83-92 ◽  
Author(s):  
Sonia Brivio ◽  
Antonio Lanteri
Keyword(s):  
Complex Projective ◽  
Hyperplane Sections ◽  
Projective Surfaces

scholarly journals CLASSIFICATION OF POISSON SURFACES

2005 ◽  
Vol 07 (01) ◽  
pp. 89-95 ◽  
Author(s):  
CLAUDIO BARTOCCI ◽  
EMANUELE MACRÌ
Keyword(s):  
Poisson Structure ◽  
Classification Theorem ◽  
Poisson Structures ◽  
Complex Projective ◽  
Projective Surfaces

We study complex projective surfaces admitting a Poisson structure; we prove a classification theorem and count how many independent Poisson structures there are on a given Poisson surface.

scholarly journals Roitman?s theorem for singular complex projective surfaces

1996 ◽  
Vol 84 (1) ◽  
pp. 155-190 ◽  
Author(s):  
L. Barbieri-Viale ◽  
C. Pedrini ◽  
C. Weibel
Keyword(s):  
Complex Projective ◽  
Projective Surfaces

scholarly journals Universal Series for Hilbert Schemes and Strange Duality

2018 ◽  
Vol 2020 (10) ◽  
pp. 3130-3152
Author(s):  
Drew Johnson
Keyword(s):  
Combinatorial Proof ◽  
Line Bundles ◽  
Del Pezzo Surfaces ◽  
Hilbert Schemes ◽  
Euler Characteristics ◽  
Quot Scheme ◽  
Del Pezzo ◽  
Complex Projective ◽  
Strange Duality ◽  
Projective Surfaces

Abstract We show how the “finite Quot scheme method” applied to Le Potier’s strange duality on del Pezzo surfaces leads to conjectures (valid for all smooth complex projective surfaces) relating two sets of universal power series on Hilbert schemes of points on surfaces: those for top Chern classes of tautological sheaves and those for Euler characteristics of line bundles. We have verified these predictions computationally for low order. We then give an analysis of these conjectures in small ranks. We also give a combinatorial proof of a formula predicted by our conjectures: the top Chern class of the tautological sheaf on $S^{[n]}$ associated to the structure sheaf of a point is equal to $(-1)^n$ times the nth Catalan number.

Recognizing singularities of surfaces in ℂP3

1982 ◽  
Vol 91 (1) ◽  
pp. 17-27 ◽  
Author(s):  
M. G. Soares ◽  
P. J. Giblin
Keyword(s):  
Projective Curves ◽  
Complex Projective ◽  
Projective Surfaces

In this paper we consider complex projective surfaces V, defined by an equation of the form fn–1 (x, y, z) w + fn (x, y, z) = 0, where fi is homogeneous of degree i, and relate the geometry of the intersections of the piane projective curves fn–1 = 0 and fn = 0 with the singularities of V. The results we obtain clarify and generalize some of those presented by Bruce and Wall (3).

On submersions of the complex indicatrix

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5081-5092
Author(s):  
Elena Popovicia
Keyword(s):  
Fixed Point ◽  
Complex Projective Space ◽  
Finsler Space ◽  
Hermitian Manifold ◽  
Almost Hermitian Manifold ◽  
Codimension One ◽  
Real Submanifold ◽  
Fundamental Equations ◽  
Complex Projective ◽  
Extrinsic Sphere

In this paper we study the complex indicatrix associated to a complex Finsler space as an embedded CR - hypersurface of the holomorphic tangent bundle, considered in a fixed point. Following the study of CR - submanifolds of a K?hler manifold, there are investigated some properties of the complex indicatrix as a real submanifold of codimension one, using the submanifold formulae and the fundamental equations. As a result, the complex indicatrix is an extrinsic sphere of the holomorphic tangent space in each fibre of a complex Finsler bundle. Also, submersions from the complex indicatrix onto an almost Hermitian manifold and some properties that can occur on them are studied. As application, an explicit submersion onto the complex projective space is provided.

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