… basic algebraic geometry, … del Pezzo surfaces, and we focus especially on del Pezzo
surfaces of degree 1 in Section 1.4. In Sections 1.1, 1.3, 1.4.1, and 1.4.3, we work with del Pezzo …

… lines for del Pezzo surfaces is deduced in a geometrical way and … del Pezzo surfaces of
degree 2 and 1, Propositions 4.1 and 5.1, follows from an easy argument of projective geometry. …

… 2.1 Preliminaries on geometry Before we consider del Pezzo surfaces let us first define the
following geometric objects and concepts. Recall that we defined a variety over a field k to be …

… Abstract Real, complex, and tropical algebraic geometry join forces in a new branch of
mathematical physics called positive geometry. We develop the positive geometry of del Pezzo …

… Second, we need explicit geometric arguments to deal with the low degree … To analyze the
curves of low anticanonical degree on a del Pezzo surface, we need a detailed description of …

… Throughout the following sections, we shall study the geometry of certain nonnormal del
Pezzo surfaces Y with irregularity h1(OY ) > 0. Such surfaces were first constructed by Reid [30]. …

… The preceding results are special cases of our analysis of del Pezzo surfaces V over
arbitrary imperfect fields F, by relating the geometry of the surface to the arithmetic of the ground …

… del Pezzo surfaces [13, 40]; they are precisely the Fano manifolds of complex dimension \(2\).
Every del Pezzo … Any del Pezzo surface is biholomorphic either to \({\mathbb {C} \mathbb {P…

… We continue the study of a class of geometric transitions … In this paper we consider an
extremal transition for a local del Pezzo … amplitudes of the local del Pezzo model to a system of …

… In this paper we view a del Pezzo surface X with quotient … some constructions by hand using
birational geometry; then, we found … a geometric explanation for the fact that some del Pezzo …