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:**BOOK**-
*Calabi-Yau Manifolds — A Bestiary for Physicists* - (World Scientific, Singapore, 1992; hardcover)
- + 2nd, corrected and expanded edition
**(World Scientific, Singapore, 1994; paperback)**[ A ] [ B ] [ WSci, DOI:10.1142/1410 ]- for reviews, see: Physics Today, 6/93, p. 93-94 (by E. Witten),

and Zentralblatt für Mathematik 771 (1993) 53002 (by J.D. Zund) [Zbl 0771.53002].

Cover photograph by*Donna D'Fini*.

(2nd, paperback edition from 1994):**ERRATA**- “p.
*n*” = page*n*; “P.*n*” = paragraph*n*; “*l*.*n*” = line*n*,*n*> 0 is counted downward ,*n*< 0 upward;

“S.*m.n*” = section*n*of chapter*m*.

If you notice any kind of error in the book, please, do 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. That is,
*χ*= 2(_{E}*b*_{1,1}–*b*_{2,1}) - p. 37, Eq. (1.3.19): the middle term should be “ =
*c*(Σ) = Π_{i}ℒ_{i}(_{i }c*ℒ*) = ”. [Philippe Spindel, thanks!]_{i} - p. 39, Eq. (1.3.27): the “ 1/
*n*! ” normalization of the integral is a convention, alas different from that in Eq. (1.3.28) and later: - The equality Eq. (1.3.27) is in agreement with Wirtinger’s theorem and inequality; see, e.g., the Wikipedia entry, p.31 or
*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 standard to omit the “ 1/*n*! ” normalization factor in intersection computations, which re-normalizes the relation between the 2*n*-volume of a hypersurface and its Euler number as given in Eq. (1.3.28). [Philippe Spindel, thanks!] - p. 42, Eqs. (1.5.5) and (1.5.6): the last terms miss a prime; “ ... ch[V ]” → “ ... ch[V' ] ”
- p. 43, Eq. (1.5.10): the last term misses a prime; “ ... ∧ td[V ]” → “ ... ∧ td[V' ] ”
- p. 44, Eqs. (1.6.1), (1.6.2) and p. 336, Eq. (L.40): The left- and right-hand sides of the
*j*-map should be swapped for the*j*-maps to be*onto/surjective*as stated. The corresponding (reverse-oriented) maps in co homology are then*into/injective*. [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. 58, S.2.2.1
*l.*–1: “ ...space if... ” → “ ...space of... ” . - p. 71,
*l.*1 below Eq. (2.5.2): “ ...arithmetic genus... ” → “ ...Todd genus... ”. - The arithmetic genus is
*p*= (–1)_{a}^{n}(χ^{h}–1) - 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 in 1990–91 and whether I did have a complete remedy, I cannot remember. However, Palka observes that the defining requirement (introductory sentence of section 3.2.1 [see the article with Paul Green]) is that “ | −*K*| is without base points ”, which if amended by [_{F}*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!] ...*however,*the “simple example” (3.2.25) on p. 91 has*C*_{1}^{3}= 0, — yet explicit calculation (following Chapters 9 and A) verifies the Hodge diamond as given in (3.2.1).*Might the assumed basepoint-freedom of the anticanonical line-bundle imply*(3.2.1)*all by itself?* - p. 86,
*l*.1: the relative sign in the definition of*genus*is negative: “ 1 + ½*C*_{1}^{n}” → “1 − ½*C*_{1}^{n}”, as well as “1 + ½*χ*” → “ 1 − ½_{E}*χ*”._{E} - p. 87, Table 3.1, last entry: “ [6||2 2 3] ” → “ [6||2 2 2] ”.
- p. 94, P.2,
*l*.4: “ consists some negative ” → “ consists of some negative ”. - 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. Thus:
- “
**P**^{3}_{(1:2:2)}≈**P**^{3}” → “**P**^{2}_{(1:2:2)}≈**P**^{2}”, “**P**^{4}_{(1:2:4:4)}≈**P**^{4}_{(1:1:2:2)}” → “**P**^{3}_{(1:2:4:4)}≈**P**^{3}_{(1:1:2:2)}” and

“**P**^{5}_{(2:3:6:12:18)}≈**P**^{5}_{(1:1:1:2:3)}” → “**P**^{4}_{(2:3:6:12:18)}≈**P**^{4}_{(1:1:1:2:3)}”. - p. 131, P.1, last line: “ only at (0:0:0:0:1) and (0:1:0:0:0). ” → “only at (0:0:0:0:1). ”.
- p. 140, Eq. (5.5.1): “
*z*_{2}” → “*z*^{2}”. - p. 163, P.3,
*l*.1: “ takes incorporates” → “ incorporates⟩ “. - p. 174, Eq. (8.1.8), penultimate row (first row for
*d*_{7}): “ ±2⟨*a,c,c,d*⟩” → “ ±2⟨*a,d,d,d*⟩ “. [Andreas Schachner, thanks!] - p. 174, Eq. (8.1.9), exponent: “ 2(
*b*_{1,1}+1)” → “ (*b*_{1,1}+1) “. [Vishnu Jejjala, thanks!] - p. 178,
*l*.2 after Eq. (8.3.4): “ 2^{6}3^{6}” → “ 2^{2}3^{2}“. - p. 179,
*l*.2 after Eq. (8.3.8): “ 2^{2}3^{4}13^{2}” → “ 2^{2}13^{2}“. - p. 184, P.–1,
*l*.–1: “ 40^{th}powers ” → “ 20^{th}powers “. - p. 210: display (A.1.6) should be
- p. 211: display (A.1.10) should be
- p. 278, P.2,
*l*.1: “ ℳ^{♯}” → “ 𝔐^{♯}” - p. 319, in the Lexicon definition of Analytic: “
*a*(_{n}*z − z*_{0}) ” → “*a*(_{n}*z − z*_{0})^{n}” - p. 329,
*l.*1 below Eq. (L.21): “ ...*arithmetic genus,*... ” → “ ...*Todd genus,*... ” - Also, “ ...
*(number)*. ” → “ ...*(number)*, while*p*is the_{a}*arithmetic genus*. ” - p. 333, Eq.(L.30): “ 𝕄
_{m}×... ” → “ 𝕄_{n}×...”.^{} - p. 335,
*l*.5: “ ∧^{(}*p–n*) ” → “ ∧^{p–n}”.^{} - p. 349, title of Ref. [37]: “ Threefolds : and Introduction ” → “ Threefolds: an Introduction
”.^{}

©2024, Tristan Hübsch