Very Ample Divisors on Rational Surfaces.
Very ample line bundles on blown-up projective varieties.
Very ampleness of multiples of principal polarization on degenerate Abelian surfaces.
Quite recently, Alexeev and Nakamura proved that if Y is a stable semi-Abelic variety (SSAV) of dimension g equipped with the ample line bundle OY(1), which deforms to a principally polarized Abelian variety, then OY(n) is very ample as soon as n ≥ 2g + 1, that is n ≥ 5 in the case of surfaces. Here it is proved, via elementary methods of projective geometry, that in the case of surfaces this bound can be improved to n ≥ 3.
Von der Zerlegung der Discriminante der cubischen Gleichung, welche die Hauptaxen einer Fläche zweiter Ordnung bestimmen, in eine Summe von Quadraten.
Weak analytic hyperbolicity of generic hypersurfaces of high degree in
In this article we prove that every entire curve in a generic hypersurface of degree in is algebraically degenerated i.e there exists a proper subvariety which contains the entire curve.
Weak positivity and the stability of certain Hilbert points, III.
Weak positivity and the stability of certain Hilbert points.
Weak positivity and the stability of certain Hilbert points, II.
Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve II
2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14J26.A 4-semigroup means a numerical semigroup whose minimum positive integer is 4. In [7] we showed that a 4-semigroup with some conditions is the Weierstrass semigroup of a ramification point on a double covering of a hyperelliptic curve. In this paper we prove that the above statement holds for every 4-semigroup.
Weighted complete intersections and lattice points.
Weighted intersection numbers on Hilbert modular surfaces
Welschinger invariants of small non-toric Del Pezzo surfaces
We give a recursive formula for purely real Welschinger invariants of the following real Del Pezzo surfaces: the projective plane blown up at real and pairs of conjugate imaginary points, where , and the real quadric blown up at pairs of conjugate imaginary points and having non-empty real part. The formula is similar to Vakil’s recursive formula [22] for Gromov–Witten invariants of these surfaces and generalizes our recursive formula [12] for purely real Welschinger invariants of real toric...
When K + (n-4) L fails to be Nef.
Which 4-manifolds are toric varieties?
Zariski surfaces [Book]
Zariski's conjecture and related problems
Zero cycles on a singular surface. I. Appendix: Chow groups of rational surfaces with rational double points.
Zero cycles on a singular surface. II.
Zero cycles on certain singular elliptic surfaces
Zéro-cycles de degré 1 sur les solides de Poonen
B. Poonen a récemment exhibé des exemples de variétés projectives et lisses de dimension 3 sur un corps de nombres qui n’ont pas de point rationnel et pour lesquelles il n’y a pas d’obstruction de Brauer–Manin après revêtement fini étale. Je montre que les variétés qu’il construit possèdent des zéro-cycles de degré 1.