RT Journal Article
T1 On the canonical rings of covers of surfaces of minimal degree
A1 Gallego Rodrigo, Francisco Javier
A1 Purnaprajna, Bangere P
AB Let S be a regular surface of general type with at worst canonical singularities and with basepoint-free canonical system. Let X be its canonical image. It is well known that X must be a canonical surface or a minimal degree surface. The main result of the authors completely describes the number and degree of the generators of the canonical ring of S in the second case. More concretely, if r = deg(X) and n is the degree of the canonical map, then (1) if n = 2 and r = 1, the canonical ring is generated in degree 1, plus one generator in degree 4; (2) in the other cases, the canonical ring is generated in degree 1, plus r(n−2) generators in degree 2 and r −1 generators in degree 3.This result, together with previous results of Ciliberto and Green, describes when the canonical ring of S is generated in degree less than or equal to 2: X is not a surface of minimal degree other than the plane and, in this last case, n 6= 2. The authors also construct a series of non-trivial examples of the theorem and prove that some expected ones do not exist. Finally, the authors apply their results to Calabi-Yau threefolds, obtaining analogous results. The key point here is that, for a Calabi-Yau threefold, the general member of a big and base-point-free linear system is a surface of general type.
PB American Mathematical Society
SN 1088-6850
YR 2003
FD 2003-03-19
LK https://hdl.handle.net/20.500.14352/49665
UL https://hdl.handle.net/20.500.14352/49665
LA eng
NO First published in Transactions of the American Mathematical Society in Volume 355, Number 7, 2003, published by the American Mathematical Society
NO MCT
NO UCM
NO General Research Fund of the University of Kansas at Lawrence
DS Docta Complutense
RD 14 jun 2025