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 The generic isogeny decomposition of the Prym Variety of a cyclic branched covering

2022 ◽  
Author(s):  
Theodosis Alexandrou
Keyword(s):  
Linear System ◽  
Branch Locus ◽  
Prym Variety ◽  
Identity Component ◽  
Branched Covering ◽  
Complete Linear System ◽  
Polarized Surface ◽  
Hyperplane Sections ◽  
General Member ◽  
Projective Surfaces

AbstractLet $$f:S'\longrightarrow S$$ f : S ′ ⟶ S be a cyclic branched covering of smooth projective surfaces over $${\mathbb {C}}$$ C whose branch locus $$\Delta \subset S$$ Δ ⊂ S is a smooth ample divisor. Pick a very ample complete linear system $$|{\mathcal {H}}|$$ | H | on S, such that the polarized surface $$(S, |{\mathcal {H}}|)$$ ( S , | H | ) is not a scroll nor has rational hyperplane sections. For the general member $$[C]\in |{\mathcal {H}}|$$ [ C ] ∈ | H | consider the $$\mu _{n}$$ μ n -equivariant isogeny decomposition of the Prym variety $${{\,\mathrm{Prym}\,}}(C'/C)$$ Prym ( C ′ / C ) of the induced covering $$f:C'{:}{=}f^{-1}(C)\longrightarrow C$$ f : C ′ : = f - 1 ( C ) ⟶ C : $$\begin{aligned} {{\,\mathrm{Prym}\,}}(C'/C)\sim \prod _{d|n,\ d\ne 1}{\mathcal {P}}_{d}(C'/C). \end{aligned}$$ Prym ( C ′ / C ) ∼ ∏ d | n , d ≠ 1 P d ( C ′ / C ) . We show that for the very general member $$[C]\in |{\mathcal {H}}|$$ [ C ] ∈ | H | the isogeny component $${\mathcal {P}}_{d}(C'/C)$$ P d ( C ′ / C ) is $$\mu _{d}$$ μ d -simple with $${{\,\mathrm{End}\,}}_{\mu _{d}}({\mathcal {P}}_{d}(C'/C))\cong {\mathbb {Z}}[\zeta _{d}]$$ End μ d ( P d ( C ′ / C ) ) ≅ Z [ ζ d ] . In addition, for the non-ample case we reformulate the result by considering the identity component of the kernel of the map $${\mathcal {P}}_{d}(C'/C)\subset {{\,\mathrm{Jac}\,}}(C')\longrightarrow {{\,\mathrm{Alb}\,}}(S')$$ P d ( C ′ / C ) ⊂ Jac ( C ′ ) ⟶ Alb ( S ′ ) .

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.

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.

On the Hyperplane Sections of Blow-Ups of Complex Projective Plane

1989 ◽  
Vol 41 (6) ◽  
pp. 1005-1020 ◽  
Author(s):  
Aldo Biancofiore
Keyword(s):  
Line Bundle ◽  
Projective Plane ◽  
Algebraic Surfaces ◽  
Projective Surface ◽  
Complex Projective Plane ◽  
Complex Projective ◽  
Hyperplane Sections

Let L be a line bundle on a connected, smooth, algebraic, projective surface X. In this paper we have studied the following questions:1) Under which conditions is L spanned by global sections? I.e., if ɸL : X →PN denotes the map associated to the space Г(L) of the sections of L, when is ɸL a morphism?2) Under which conditions is L very ample? I.e., when does ɸL give an embedding?These problems arise naturally in the study, and in particular in the classification, of algebraic surfaces (see [8], [3], [5]).

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).

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