Results 1  10
of
135,632
THE ENUMERATIVE GEOMETRY OF DEL PEZZO SURFACES
"... Abstract. This paper investigates lowcodimension degenerations of Del Pezzo surfaces. As an application we determine certain characteristic numbers of Del Pezzo surfaces. Finally, we analyze the relation between the enumerative geometry of Del Pezzo surfaces and the GromovWitten invariants of the ..."
Abstract
 Add to MetaCart
Abstract. This paper investigates lowcodimension degenerations of Del Pezzo surfaces. As an application we determine certain characteristic numbers of Del Pezzo surfaces. Finally, we analyze the relation between the enumerative geometry of Del Pezzo surfaces and the GromovWitten invariants
Nonnormal del Pezzo surfaces
 Publications of RIMS, Kyoto
, 1994
"... 0.1 Throughout this paper, a del Pezzo surface is by definition a connected, 2dimensional, projective kscheme X, OX(1) that is Gorenstein and anticanonically polarised; in other words, X is Cohen–Macaulay, and the dualising sheaf is invertible and antiample: ωX ∼ = OX(−1). For example, X = X3 ⊂ P ..."
Abstract

Cited by 37 (4 self)
 Add to MetaCart
0.1 Throughout this paper, a del Pezzo surface is by definition a connected, 2dimensional, projective kscheme X, OX(1) that is Gorenstein and anticanonically polarised; in other words, X is Cohen–Macaulay, and the dualising sheaf is invertible and antiample: ωX ∼ = OX(−1). For example, X = X3
Tropicalization of Del Pezzo Surfaces
"... We determine the tropicalizations of very affine surfaces over a valued field that are obtained from del Pezzo surfaces of degree 5, 4 and 3 by removing their (−1)curves. On these tropical surfaces, the boundary divisors are represented by trees at infinity. These trees are glued together according ..."
Abstract
 Add to MetaCart
We determine the tropicalizations of very affine surfaces over a valued field that are obtained from del Pezzo surfaces of degree 5, 4 and 3 by removing their (−1)curves. On these tropical surfaces, the boundary divisors are represented by trees at infinity. These trees are glued together
On Gorenstein log del Pezzo surfaces
 Japan. J. Math
"... In this paper, we first present the complete list of the singularity types of the Picard number one Gorenstein log del Pezzo surface and the number of the isomorphism classes with the given singularity type. Then we give out a method to find out all singularity types of Gorenstein log del Pezzo surf ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
In this paper, we first present the complete list of the singularity types of the Picard number one Gorenstein log del Pezzo surface and the number of the isomorphism classes with the given singularity type. Then we give out a method to find out all singularity types of Gorenstein log del Pezzo
WEAK DEL PEZZO SURFACES WITH IRREGULARITY
, 2007
"... Abstract. I construct normal del Pezzo surfaces, and regular weak del Pezzo surfaces as well, with positive irregularity q> 0. This can happen only over nonperfect fields. The surfaces in question are twisted forms of nonnormal del Pezzo surfaces, which were classified by Reid. The twisting is wi ..."
Abstract
 Add to MetaCart
Abstract. I construct normal del Pezzo surfaces, and regular weak del Pezzo surfaces as well, with positive irregularity q> 0. This can happen only over nonperfect fields. The surfaces in question are twisted forms of nonnormal del Pezzo surfaces, which were classified by Reid. The twisting
Del Pezzo surfaces and representation theory
, 2006
"... Del Pezzo surfaces, classically defined as smooth surfaces of degree d in the projective space P d, are among the most studied and best understood of algebraic varieties. ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Del Pezzo surfaces, classically defined as smooth surfaces of degree d in the projective space P d, are among the most studied and best understood of algebraic varieties.
Exceptional curves on Del Pezzo surfaces
 Math. Nachr
, 2003
"... We classify all cases of exceptional curves on Del Pezzo surfaces, which turn out to be the smooth plane curves and some other cases with Clifford dimension 3. Moreover, the property of being exceptional holds for all curves in the complete linear system. We use this study to extend the results of P ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We classify all cases of exceptional curves on Del Pezzo surfaces, which turn out to be the smooth plane curves and some other cases with Clifford dimension 3. Moreover, the property of being exceptional holds for all curves in the complete linear system. We use this study to extend the results
Del Pezzo Surfaces and Semiregular Polytopes
, 2009
"... In this article, we research on the correspondences between the geometry of del Pezzo surfaces Sr and the geometry of Gosset polytopes (r−4)21. We study skew alines(a ≤ r), exceptional systems and rulings, and we explain their correspondences to (a − 1)simplexes, (r − 1)simplexes and (r − 1)cros ..."
Abstract
 Add to MetaCart
In this article, we research on the correspondences between the geometry of del Pezzo surfaces Sr and the geometry of Gosset polytopes (r−4)21. We study skew alines(a ≤ r), exceptional systems and rulings, and we explain their correspondences to (a − 1)simplexes, (r − 1)simplexes and (r − 1
Regular del Pezzo surfaces with irregularity
 J. Alg. Geom
, 2014
"... ABSTRACT. We construct the first examples of regular del Pezzo surfacesX for which h1(X,OX)> 0. We also find a restriction on the integer pairs that are possible as the anticanonical degree K2X and irregularity h1(X,OX) of such a surface. CONTENTS ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
ABSTRACT. We construct the first examples of regular del Pezzo surfacesX for which h1(X,OX)> 0. We also find a restriction on the integer pairs that are possible as the anticanonical degree K2X and irregularity h1(X,OX) of such a surface. CONTENTS
On the Cox Ring of Del Pezzo Surfaces
, 2006
"... Let Sr be the blowup of P² in r general points, i.e., a smooth Del Pezzo surface of degree 9 − r. For r ≤ 7, we determine the quadratic equations defining its Cox ring explicitly. The ideal of the relations in Cox(S8) is calculated up to radical. As conjectured by ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
Let Sr be the blowup of P² in r general points, i.e., a smooth Del Pezzo surface of degree 9 − r. For r ≤ 7, we determine the quadratic equations defining its Cox ring explicitly. The ideal of the relations in Cox(S8) is calculated up to radical. As conjectured by
Results 1  10
of
135,632