RT Journal Article
T1 Classification of quadruple Galois canonical covers, II
A1 Gallego Rodrigo, Francisco Javier
A1 Purnaprajna, Bangere P.
AB In this article we classify quadruple Galois canonical covers ϕ of singular surfaces of minimal degree.This complements the work done in [F.J. Gallego, B.P. Purnaprajna, Classification of quadruple Galois canonical covers, I, preprint, math.AG/0302045], so the main output of both papers is the complete classification of quadruple Galois canonical covers of surfaces of minimal degree, both singular and smooth.Our results show that the covers X studied in this article are all regular surfaces and form a bounded family in terms of geometric genus pg. This is in sharp contrast to the results, shown in [F.J. Gallego, B.P. Purnaprajna, Classification of quadruple Galois canonical covers, I, preprint, math.AG/0302045], on the unboundedness of pg and q for covers of smooth surfaces of minimal degree.In fact, the geometric genus of X is bounded by 4. Together with the results of Horikawa and Konno for double and triple covers, a striking numerology emerges that motivates some general questions on the existence of higher degree canonical covers. In this article, we also answer some of these questions. The arguments to prove our results include a delicate analysis of the discrepancies of partial resolutions of X and of the ramification and inertia groups o
PB Academic Press
SN 0021-8693
YR 2007
FD 2007
LK https://hdl.handle.net/20.500.14352/49956
UL https://hdl.handle.net/20.500.14352/49956
LA eng
NO H. Clemens, J. Kollár, S. Mori, Higher dimensional complex geometry, Astérisque 166 (1988).F.J. Gallego, B.P. Purnaprajna, On the canonical ring of covers of surfaces of minimal degree, Trans. Amer.Math. Soc. 355 (2003) 2715–2732.F.J. Gallego, B.P. Purnaprajna, Classification of quadruple Galois canonical covers, I, preprint, math.AG/0302045.F.J. Gallego, B.P. Purnaprajna, Classification of quadruple canonical covers: Galois case, C. R. Math. Acad. Sci.Soc. R. Can. 26 (2) (2004) 45–50.D. Hahn, R. Miranda, Quadruple covers of algebraic varieties, J. Algebraic Geom. 8 (1999) 1–30.
NO MCT
NO NSA
DS Docta Complutense
RD 18 abr 2024