Some algebraic surfaces with canonical map of degree 10, 12, 14
نویسندگان
چکیده
Surfaces of general type with canonical map degree d bigger than 8 have bounded geometric genus and irregularity. In particular the irregularity is at most 2 if d≥10. present paper, existence surfaces = 10 all possible irregularities, 12 1 2, 14 0 proven, by constructing these as Z23-covers certain rational surfaces. These results together construction C. Rito a surface show that possibilities for in cases 10, can occur, whilst still an open problem.
منابع مشابه
Complex Algebraic Surfaces Class 14
Useful proposition. Consider the blow-up of P at n general points, giving exceptional divisors E1, : : : , En. Then the intersection ring on P is given by Z[H;E1; : : : ; En]=H 2 = 1; HEi = 0; Ei Ej = 0; E 2 i = 1: We can understand divisors and sections of divisors in terms of divisors on P with certain multiplicities at the Ej . More precisely: the vector space of sections of aH b1E1 bnEn is ...
متن کاملComplex Algebraic Surfaces Class 12
(i) is the most important one. We showed that extensions < = are classified by >@?A& 1 B DCE GF ( . The element 0 corresponded to a splitting. If one element is a non-zero multiple of the other, they correspond to the same , although different extensions. As an application, we proved: Proposition. Every rank 2 locally free sheaf on ? is a direct sum of invertible sheaves. I can’t remember if I ...
متن کاملComplex Algebraic Surfaces Class 10
Clearly (b) implies (a) implies geometrically ruled. The theorem we’re in the process of proving is: Noether-Enriques Theorem. Suppose π : S → C is geometrically ruled. Then S is of type (b) above, i.e. it is the projectivization of some rank 2 invertible sheaf / vector bundle. We’re proving more generally: Suppose π : S → C, and x ∈ C such π is smooth over C and π−1(x) is isomorphic to P. Then...
متن کاملCanonical Symplectic Structures and Deformations of Algebraic Surfaces
We show that a minimal surface of general type has a canonical symplectic structure (unique up to symplectomorphism) which is invariant for smooth deformation. Our main theorem is that the symplectomorphism type is also invariant for deformations which allow certain normal singular-ities, called Single Smoothing Singularities (and abbreviated as SSS), and moreover for deformations yielding Q-Go...
متن کاملSpin Canonical Invariants of 4-manifolds and Algebraic Surfaces
Donaldson’s celebrated construction of polynomial invariants for 4-manifolds (see for example [D–K]) has served as a model for an enormous range of recent results and constructions relating algebraic geometry and differential topology. The short written version of Donaldson’s talk at the 1990 Arbeitstagung contained the construction of jumping instantons, and was the starting point for our cons...
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: Communications in Algebra
سال: 2023
ISSN: ['1532-4125', '0092-7872']
DOI: https://doi.org/10.1080/00927872.2023.2232869