Remember that a pair (X, [DELTA]) is called log surface if X is a normal algebraic surface
and [DELTA] is a boundary R-divisor on X such that [K.sub.X] + [DELTA] is R-Cartier (See [Fjn12, Definition 3.1]).
(4) We see that the locus is an algebraic surface
of third degree.
A real elliptic surface will be a morphism [[PI].sub.1] : Y [right arrow] [P.sup.1] defined over R, when Y is a real algebraic surface
such that over all but finitely many points in the basic curve, the fibre is a nonsingular curve of genus one.
Topics include algebraic curve theory, algebraic surface
theory, moduli space, automorphic forms, Mordell-Weil lattices and automorphisms of hyperkahler manifolds.
Let X be an algebraic surface
with isolated normal singularities, [pi]: V [right arrow] X its minimal resolution, and E the reduced exceptional divisor.
Let X be a projective algebraic surface
(over C) with an ample line bundle L.
Let X be a normal algebraic surface
and let [DELTA] be a boundary R-divisor on X such that [K.sub.X] + [DELTA] is R-Cartier.
Zariski, The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface
Goto, A Public-key Cryptosystem using Algebraic Surfaces
: Extended Abstract, PQCrypto Workshop Record, 2006.
Shigefumi Mori, 39, of Kyoto University, has devoted much of his career to pioneering methods of classifying certain kinds of surfaces defined by algebraic equations, thereby extending the classical theory of algebraic surfaces
to three dimensions.
Using this result, new methods for blending several algebraic surfaces
simultaneously are derived.