Ulrich trichotomy on del Pezzo surfaces
نویسندگان
چکیده
Abstract We use a correspondence between Ulrich bundles on projective variety and quiver representations to prove that certain del Pezzo surfaces satisfy the trichotomy, for any given polarization.
منابع مشابه
Nonnormal Del Pezzo Surfaces
0.1 Throughout this paper, a del Pezzo surface is by definition a connected, 2-dimensional, projective k-scheme 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 3 an arbitrary hypersurface of degree 3. Under extra conditions, del Pezzo surfaces are interesting...
متن کاملBihermitian metrics on Del Pezzo surfaces
Recall that a Del Pezzo surface is defined as an algebraic surface with ample anticanonical bundle K. Ampleness means that the line bundle K has a hermitian metric whose curvature form F is positive, defining a Kähler metric g0. This is the data for our construction – we take a holomorphic section σ of K, and the function f = log ‖σ‖. This function is singular on the zero set of σ (which is an ...
متن کاملArithmetic on Singular Del Pezzo Surfaces
The study of singular cubic surfaces is quite an old subject, since their classification (over C) goes back to Schlafli [39] and Cay ley [8]. However, a recent account by Bruce and Wall [6] has shown that modern singularity theory can give much insight into this classification. One of the main themes of the present paper is that this approach is also useful over an arbitrary perfect field k for...
متن کاملDel Pezzo Surfaces with Du Val Singularities
In this paper we show that del Pezzo surfaces of degree 1 with Du Val singular points of type A4, A4 + A4, A4 + A3, A4 + 2A1, A4 + A1, A3 + 4A1, A3 + 3A1, 2A3 + 2A1, A3 + 2A1, A3 + A1, 2A3, A3, admit a Kähler-Einstein metric. Moreover we are going to compute global log canonical thresholds of del Pezzo surfaces of degree 1 with Du Val singularities, and of del Pezzo surfaces of Picard group Z w...
متن کاملLagrangian Spheres in Del Pezzo Surfaces
Lagrangian spheres in the symplectic Del Pezzo surfaces arising as blow-ups of CP in 4 or fewer points are classified up to Lagrangian isotopy. Unlike the case of the 5-point blow-up, there is no Lagrangian knotting.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Geometry
سال: 2023
ISSN: ['1615-715X', '1615-7168']
DOI: https://doi.org/10.1515/advgeom-2022-0024