List of Works:
1. The intersection of two quadrics, Ph.D. Thesis, Cambridge 1972 (unpublished)
www.maths.warwick.ac.uk/~miles/3folds/qu.pdf
2. Hyperelliptic linear systems on a K3 surface, J. London Math. Soc. (2) 13
(1976), 427--437
www.maths.warwick.ac.uk/~miles/Reprint/hellK3.pdf
3. Special linear systems on curves lying on a K3 surface, J. London Math. Soc.
(2) 13 (1976), 454--458
www.maths.warwick.ac.uk/~miles/Reprint/sK3.pdf
4. Elliptic Gorenstein surface singularities, 1975 (unpublished)
www.maths.warwick.ac.uk/~miles/surf/eG.ps (figures incomplete)
5. Bogomolov's theorem c_1^2 <= 4c_2, in Proc. international symp. on
algebraic geometry, Kyoto, Kinokuniya 1977, 623--642
www.maths.warwick.ac.uk/~miles/Reprint/Bogomolov.pdf
6. Surfaces with p_g = 0, K^2 = 1, J. Fac. Sci. Tokyo Univ. 25 (1978), 75--92
www.maths.warwick.ac.uk/~miles/Reprint/pg0K21.pdf
7. Surfaces with p_g = 0, K^2 = 2, 1978 (unpublished)
www.maths.warwick.ac.uk/~miles/surf/K2=2.ps (incomplete)
8. pi_1 for surfaces with small K^2, in Algebraic geometry (Copenhagen,
1978), Springer LNM 732, 1979, 534--544
www.maths.warwick.ac.uk/~miles/Reprint/pi_1.pdf
9. Canonical 3--folds, in Journee's de ge'ome'trie alge'brique d'Angers, ed.
A. Beauville, Sijthoff and Noordhoff, Alphen 1980, 273--310
10. Lines on Fano 3--folds according to Shokurov, Mittag-Leffler Inst. report
1980 No. 11 (unpublished)
www.maths.warwick.ac.uk/~miles/Unpub/five_early/Shok.ps (errors to fix)
11. Minimal models of canonical 3--folds, in Advanced studies in Pure Math. 1,
Analytic varieties and algebraic varieties, ed. S. Iitaka, Kinokuniya and
North-Holland, 1983, 131--180
12. Decomposition of toric morphisms, in Arithmetic and Geometry, papers
dedicated to I.R. Shafarevich, Birkha"user 1983, Vol II, 395--418
13. Projective morphisms according to Kawamata, Warwick preprint, 1983
(unpublished) www.maths.warwick.ac.uk/~miles/3folds/Ka.pdf
14. Surfaces of small degree, Math. Annalen. 275 (1986), 71--80
15. Tendencious survey of 3-folds, in Algebraic Geometry, Bowdoin 1985, ed. S.
Bloch, Proc. of Symposia in Pure Math. 46, A.M.S. (1987), vol. 1, 333--344
16. Young person's guide to canonical singularities, in Algebraic Geometry,
Bowdoin 1985, ed. S. Bloch, Proc. of Symposia in Pure Math. 46, A.M.S. (1987),
vol. 1, 345--414
17. Undergraduate algebraic geometry, LMS student text series, C.U.P. 1988
(pp. 129 + viii); Russian edition Mir, Moscow 1991; Japanese edition
Iwanami, Tokyo 1991 (pp. 213 + ix); Chinese edition Shaanxi Normal Univ.
press, 1992 (ISBN 7-5613-0648-2, 2.90 RMB); Persian edition Tehran, 1997
(pp. 166 + vii)); Spanish edition by Tomas Lajous in preparation
18. The moduli space of 3-folds with K = 0 may nevertheless be irreducible, in
Hirzebruch Festschrift, Math. Ann. 278 (1987), 329--334
19. Quadrics through a canonical surface, in: Algebraic Geometry -- Hyperplane
sections and related topics (L'Aquila 1988), Springer LNM 1417 (1990), 191--213
www.maths.warwick.ac.uk/~miles/Reprint/quads.pdf
20. Infinitesimal view of extending a hyperplane section, in: Algebraic
Geometry -- Hyperplane sections and related topics (L'Aquila 1988), Springer
LNM 1417 (1990), 214--286
www.maths.warwick.ac.uk/~miles/Reprint/hyperplane.pdf
21. Campedelli versus Godeaux, in Problems in the theory of surfaces and their
classification, (Cortona, Oct 1988), F. Catanese and others Eds., Academic
Press 1991, 309--366
22. Surfaces with p_g = 3, K^2 = 4 according to E. Horikawa and D. Dicks, in
Proceedings of Algebraic geometry mini-symposium (Tokyo Univ., Dec 1989,
distributed in Japan only), 1--22. (See my website + surfaces)
23. Nonnormal del Pezzo surfaces, Math Proc. RIMS 30 (1994), 695--727
24. Undergraduate Commutative Algebra, LMS student text series 28, C.U.P., Nov
1995, (pp. 153 + xviii), (Japanese edition, Iwanami Tokyo, Mar 2000)
25. (with Y. Ito) The McKay correspondence for finite subgroups of SL(3, C),
in Higher dimensional complex varieties (Trento, Jun 1994), M. Andreatta and
others Eds., de Gruyter, 1996, 221--240
26. Chapters on algebraic surfaces, in Complex algebraic varieties, J.
Koll\'ar Ed., IAS/Park City lecture notes series (1993 volume), AMS,
1997, 1--154. (See my website + surfaces)
27. (with F. Catanese, M. Franciosi and K. Hulek), Embeddings of curves and
surfaces, Nagoya Math. J. 154 (1999), 185--220
28. Graded rings over K3 surfaces, in abstracts of Matsumura memorial
conference (Nagoya, Aug 1996), 11 pp. (See my website + surfaces)
29. McKay correspondence, in Proc. of algebraic geometry symposium (Kinosaki,
Nov 1996), T. Katsura (Ed.), 14--41, Duke file server alg-geom 9702016, 30 pp.,
rejected by Geometry and Topology
30. (with Tom Bridgeland and Alastair King), Mukai implies McKay: the McKay
correspondence as an equivalence of derived categories, J. Amer. Math. Soc.,
14 (2001), 535--554, preprint math/9908027, 27 pp.
31. (with Alastair Craw), How to calculate A-Hilb C^3, in Geometry of toric
varieties (Grenoble, 2000), collection S\'emin. Congr., {\bf6} SMF 2002,
pp.~129--154; preprint math.AG/9909085
32. La correspondance de McKay, S\'eminaire Bourbaki, 52\`eme ann\'ee,
novembre 1999, no. 867, Ast\'erisque 276 (2002), 53--72 preprint
math/9911165, 20 pp.
33. (with A. Corti and A. Pukhlikov), Birationally rigid Fano hypersurfaces,
in Explicit birational geometry of 3-folds, A. Corti and M. Reid (eds.), CUP
2000, 175--258
34. 25 years of 3-folds -- and old person's view, in Explicit birational
geometry of 3-folds, A. Corti and M. Reid (eds.), CUP 2000, 313--343
35. (with S. Papadakis), Kustin-Miller unprojection without complexes,
J. Algebraic Geom. 13 (2004), 563-577, preprint math.AG/0011094, 18 pp.
36. Graded rings and birational geometry, in Proc. of algebraic geometry
symposium (Kinosaki, Oct 2000), K. Ohno (Ed.), 1--72. (See my website +
3-folds)
37. Examples of Type IV unprojection, math.AG/0108037, 16 pp.
38. (with S. Alt{\i}nok and G. Brown), Fano 3-folds, K3 surfaces and graded
rings, in Topology and geometry: commemorating SISTAG (National Univ. of
Singapore, 2001), Ed. A. J. Berrick and others, Contemp. Math. 314, AMS,
2002, pp. 25--53, preprint math.AG/0202092, 29 pp.
39. (with A. Corti), Weighted Grassmannians, in Algebraic Geometry (Genova,
Sep 2001), In memory of Paolo Francia, M. Beltrametti and F. Catanese Eds.,
de Gruyter, Berlin, 2002, 141--163, preprint math.AG/0206011, 27 pp.
40. Update on 3-folds, Proc. of the ICM 2002, vol. II, pp. 513--524, preprint
math.AG/0206157, 14 pp.
41. (with Kaori Suzuki), Cascades of projections from log del Pezzo surfaces,
in Number theory and algebraic geometry -- to Peter Swinnerton-Dyer on his
75th birthday, Alexei N Skorobogatov and Miles Reid editors, CUP 2003,
pp. 227--249
42. Constructing algebraic varieties via commutative algebra, in Proc.
of 4th European Congress of Math (Stockholm 2004), European Math Soc.
2005, pp. 655--667 13 pp., preprint available from
http://www.maths.warwick.ac.uk/~miles/surf/
43. (with Balazs Szendroi) Geometry and Topology, CUP Nov 2005,
ISBN 0521613256, pp. 241 + xxii
44. (with Margarida Mendes Lopes and Rita Pardini), Campedelli surfaces
with fundamental group of order 8, Geometriae Dedicata 139 (2009)
49--55, preprint: arXiv 0805.0006, 10 pp.
45. (with Gavin Brown and Michael Kerber), Fano 3-folds in codimension 4,
Tom and Jerry, Part I, Compositio Math 148 (2012), 1171-1194, preprint
arXiv:1009.4313, 33 pp.
46. (with Yuri Prokhorov), On Q-Fano threefolds of Fano index 2, in
Minimal Models and Extremal Rays (Kyoto 2011), Advanced Studies in Pure
Mathematics 70, 2016, pp. 397--420, preprint arXiv:1203.0852, 22 pp.
47. Gorenstein in codimension 4 - the general structure theory,
Algebraic Geometry in East Asia (Taibei Nov 2011), Advanced Studies in
Pure Mathematics 65 (2015) pp. 201-227, preprint arXiv:1304.5248, 30 pp.
48. (with Anita Buckley and Shengtian Zhou), Ice cream and orbifold
Riemann-Roch, Izvestiya RAN. Seriya Matematicheskaya 77:3-4 (2013),
461--486 issue dedicated to I.R. Shafarevich, preprint arXiv:1208.0457, 29 pp.
49. (with Gavin Brown), Diptych varieties. I, Proceedings of the London
Math Society 107 (6) (2013), 1353-1394. preprint arXiv:1208.2446, 50 pp.
50. (with Gavin Brown), Diptych varieties. II, Apolar varieties, Higher
Dimensional Algebraic Geometry (Kawamata 60), Advanced Studies in Pure
Mathematics 74 (2017) pp. 41--72, preprint arXiv:1208.5858, 23 pp.
51. (with Gavin Brown and Jan Stevens), Tutorial on Tom and Jerry: the two
smoothings of the anticanonical cone over PP(1,2,3), EMS Surv. Math. Sci.
8 (2021) 25–38, arXiv:1812.02594, 12 pp.
52. The Tate-Oort group scheme TOp, Proc. Steklov Inst. Math. 307 (2019),
245--266, get from http://www.warwick.ac.uk/~masda/TOp/
Book translations:
=================
T1. H. Matsumura, Commutative ring theory, Cambridge studies in advanced
mathematics 8, C.U.P., 1986 (pp. 320 + xiii)
T2. V.V. Nikulin and I.R. Shafarevich, Geometries and groups, Springer
Universitext, 1987 (pp. 251 + viii) (Japanese translation Springer Tokyo, 1993
(pp. 304 + xiii))
T3. I.R. Shafarevich, Basic notions of algebra, Encyclopaedia of Mathematics
11, Springer, 1990 (pp. iv+258) ISBN: 3-540-61221-1
T4. I.R. Shafarevich, Basic algebraic geometry, Second edition (revised and
supplemented), Springer Verlag, 1994, 2 volumes, (pp. 303 + xviii and pp. 269 +
xiv) (Japanese translation, Springer Tokyo). Third edition, Springer 2013
T5. E. Date, M. Jimbo and T. Miwa, Solitons: Differential equations,
symmetries and infinite dimensional algebras (Iwanami, 1992), Cambridge tracts
in math. 135, CUP 2000, 108 pp. + ix
Books edited:
============
B1. Klaus Hulek (chief editor), Fabrizio Catanese, Chris Peters, Miles Reid
(editors), New Trends in Algebraic Geometry -- EuroConference on Algebraic
Geometry (Warwick, July 1996), CUP/LMS lecture notes 1999, pp. 483 + viii
ISBN: 0-521-64659-6
B2. A. Corti and M. Reid (editors), Explicit birational geometry of 3-folds,
CUP/LMS lecture notes 2000, pp. 349 + v
B3. Alexei N Skorobogatov and Miles Reid (editors), Number theory and
algebraic geometry -- to Peter Swinnerton-Dyer on his 75th birthday, CUP
2003, 300 pp. + vi
Work currently in progress:
==========================
P0. M. Reid, Five early pieces (a volume in preparation containing the
unpublished works [1, 4, 7, 10, 13]). See
http://www.maths.warwick.ac.uk/~miles/Unpub/ + Five early pieces
P1. More chapters on algebraic surfaces (sequel to [26]), projected book,
currently approx 200 pp. See my website + surfaces.
P2. What is a flip? preprint and lecture notes. See my website +
3-folds + What is a flip?
P3. (with Colin Ingalls) A 3-torsion Brauer class over PP^2, currently
15 pp.
P4. (with Gavin Brown) Diptych varieties and Mori flips of Type A,
Parts III and IV, currently 35 pp. plus 50 pp. of notes. See website
http://www-staff.lboro.ac.uk/~magdb/diptych.html
P5. (with Gavin Brown) Extreme K3 surfaces and high Type II unprojections,
currently 10 pp.
P6. (with Becky Leng and Magda Sebestean) Trihedral G-Hilb, currently 12 pp.
P7. (with Stavros Papadakis) Quasi-Gorenstein unprojection, currently 20 pp.
P9. Relative fractional canonical algebras and the general Godeaux surface,
currently 48 pp.
P10. (with Sarah Davis and Timothy Logvinenko), How to calculate A-Hilb CC^n
for 1/r(a,b,1,..,1), 37 pp., submitted to the Rendiconti del Circolo
Matematico di Palermo, special volume dedicated to Algebraic Geometry.
Available from Traps website
http://www.cantab.net/users/t.logvinenko/Traps