for
reviews, see: Physics Today, 6/93, p.93-94 (by
E.Witten),
and Zentralblatt für Mathematik 773
(1993)#53002 (by J.D.Zund).
Cover photograph by Donna D'Fini.
An
unsolicited opinion
: “If you have ever wanted an explicit answer to the
question,
‘What, exactly, is a Calabi-Yau manifold?’, this is
the
book you are looking for. Clear, far-ranging and full of brilliant
insight, it is also a stylisitic masterpiece, which is rare among math
and physics books.” (rick1138, 11-04-2003, 11:39 PM)
ERRATA (2nd,
paperback edition from 1994):
“p.n” = page n,
“P.n” = paragraph n,
“l.n” = line n, n > 0 is
counted downward , n
< 0 upward; “S.n” =
section n.
If you notice any kind of error in the Bestiary, please, let me know!
p. 15, l.–2, (end of S.0.4):
“ understood n” →
“ understood modulo n ”.
p. 32, Eq. (1.2.15): the right-hand side should have an
overall minus.
p. 37, Eq. (1.3.19): the middle term should be “ = c(∑_{i} L_{i}) = ∏_{i
}c(L_{i}) = ”. [Philippe Spindel,
thanks!]
p. 39, Eq. (1.3.27): the “ 1/n! ”
normalization of the integral as given is in agreement with Wirtinger’s
theorem and inequality; see, e.g., the Wikipedia entry, p.31 of Principles of
Algebraic Geometry by P.Griffiths and J.Harris (John Wiley &
Sons, 1978) or S.3.1, p.136 of Intrduction to Complex Analysis
by E.M.Chirka, P.Dolbeault, G.M.Khenkin and A.G. Vitushkin (Springer,
1997). However, it is also possible to omit the “
1/n! ” normalization, re-normalizing the relation
between the 2n-volume of a hypersurface in Eq. (1.3.28)
and its Euler number in Eq. (1.3.28) from what is implied in the
text. [Philippe
Spindel, thanks!]
p. 44, Eqs. (1.6.1) and (1.6.1): “ onto
”
→
“ into ”. [Nick
Warner, thanks!]
p. 50, Eq. (2.1.16): “ r +1”→
“ r =1 ” in the lower limit of
the 1st summation. [Philippe Spindel,
thanks!]
p. 83, footnote: The Kodaira-Nakano theorem is not applicable as
needed. [Karol
Palka, thanks!]
The Kodaira-Nakano theorem guarantees (3.2.1) for Fano
3-folds, but not for almost-Fano 3-folds that are not also
Fano, the anti-canonical bundle of which is almost ample not ample. Just how
I indended to remedy this 18 years ago and whether I did have a
complete remedy, I don’t remember. However, Palka
observes that the defining requirement (introductory sentence of
section 3.2.1 [see the article
with Paul Green]) is that “ |–K_{F}| is without base
points ”, which (when amended by K^{3}≠0) is stronger
than Miles Reid’s definition of weak Fano,
for the latter of which already the vanishing theorem by Kawamata &
Vieweg does guarantee (3.2.1). [Karol Palka, thanks!]
p. 86, l.1: the relative sign in the definition of genus is negative: “1+^{1}/_{2}C_{1}^{n}”
→ “1–^{1}/_{2}C_{1}^{n}”, as well as “1+^{1}/_{2}χ_{E}”
→ “1–^{1}/_{2}χ_{E}”.
p. 94, P.2, l.4: “consists some
negative”
→ “consists of some negative”.
p. 97, last line of S.3.3.2:
“ = (1,1|2,2,2,2) ”
→ “ = (1,1|2,2,2) ”.
p. 127, Paragraph
after Lemma 5.1 (Delorme): The dimensions of
the first
six (weighted) projective spaces in this paragraph are one less than
indicated.