<s>
In	O
mathematics	O
,	O
and	O
in	O
particular	O
differential	B-Language
geometry	I-Language
and	O
complex	O
geometry	O
,	O
a	O
complex	B-Algorithm
analytic	I-Algorithm
variety	I-Algorithm
or	O
complex	B-Algorithm
analytic	I-Algorithm
space	I-Algorithm
is	O
a	O
generalization	O
of	O
a	O
complex	O
manifold	O
which	O
allows	O
the	O
presence	O
of	O
singularities	O
.	O
</s>
<s>
Complex	B-Algorithm
analytic	I-Algorithm
varieties	I-Algorithm
are	O
locally	O
ringed	O
spaces	O
which	O
are	O
locally	O
isomorphic	O
to	O
local	O
model	O
spaces	O
,	O
where	O
a	O
local	O
model	O
space	O
is	O
an	O
open	O
subset	O
of	O
the	O
vanishing	O
locus	O
of	O
a	O
finite	O
set	O
of	O
holomorphic	O
functions	O
.	O
</s>
<s>
A	O
complex	B-Algorithm
analytic	I-Algorithm
variety	I-Algorithm
is	O
a	O
locally	O
ringed	O
-space	O
which	O
is	O
locally	O
isomorphic	O
to	O
a	O
local	O
model	O
space	O
.	O
</s>
<s>
Morphisms	O
of	O
complex	B-Algorithm
analytic	I-Algorithm
varieties	I-Algorithm
are	O
defined	O
to	O
be	O
morphisms	O
of	O
the	O
underlying	O
locally	O
ringed	O
spaces	O
,	O
they	O
are	O
also	O
called	O
holomorphic	O
maps	O
.	O
</s>
<s>
and	O
also	O
,	O
when	O
the	O
complex	B-Algorithm
analytic	I-Algorithm
space	I-Algorithm
whose	O
structure	O
sheaf	O
is	O
reduced	O
,	O
then	O
the	O
complex	B-Algorithm
analytic	I-Algorithm
space	I-Algorithm
is	O
reduced	O
,	O
that	O
is	O
,	O
the	O
complex	B-Algorithm
analytic	I-Algorithm
space	I-Algorithm
may	O
not	O
be	O
reduced	O
.	O
</s>
<s>
An	O
associated	O
complex	B-Algorithm
analytic	I-Algorithm
space	I-Algorithm
(	O
variety	O
)	O
is	O
such	O
that	O
;	O
</s>
<s>
Here	O
,	O
scheme	O
X	O
obtained	O
by	O
glueing	O
the	O
data	O
of	O
the	O
set	O
,	O
and	O
then	O
the	O
same	O
data	O
can	O
be	O
used	O
to	O
glueing	O
the	O
complex	B-Algorithm
analytic	I-Algorithm
space	I-Algorithm
into	O
an	O
complex	B-Algorithm
analytic	I-Algorithm
space	I-Algorithm
,	O
so	O
we	O
call	O
a	O
associated	O
complex	B-Algorithm
analytic	I-Algorithm
space	I-Algorithm
with	O
X	O
.	O
</s>
<s>
The	O
complex	B-Algorithm
analytic	I-Algorithm
space	I-Algorithm
X	O
is	O
reduced	O
if	O
and	O
only	O
if	O
the	O
associated	O
complex	B-Algorithm
analytic	I-Algorithm
space	I-Algorithm
reduced	O
.	O
</s>
