Preface |
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xi | |
Terminology |
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xv | |
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1 | (56) |
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1 | (2) |
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3 | (4) |
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1.3 Tangency and polarity |
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7 | (6) |
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13 | (6) |
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1.5 Numbers of subspaces on a quadric |
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19 | (2) |
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1.6 The orthogonal groups |
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21 | (8) |
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1.7 The polarity reconsidered |
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29 | (2) |
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1.8 Sections of non-singular quadrics |
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31 | (8) |
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1.9 Parabolic sections of parabolic quadrics |
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39 | (3) |
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1.10 The characterisation of quadrics |
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42 | (9) |
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1.11 Further characterisations of quadrics |
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51 | (2) |
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1.12 The Principle of Triality |
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53 | (2) |
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1.13 Generalised hexagons |
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55 | (1) |
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1.14 Notes and references |
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56 | (1) |
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57 | (42) |
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57 | (1) |
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2.2 Tangency and polarity |
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58 | (6) |
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2.3 Generators and sub-generators |
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64 | (1) |
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65 | (4) |
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2.5 The characterisation of Hermitian varieties |
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69 | (11) |
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2.6 The characterisation of projections of quadrics |
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80 | (16) |
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96 | (3) |
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99 | (44) |
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3.1 Plucker and Grassmann coordinates |
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99 | (8) |
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107 | (14) |
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3.3 A characterisation of Grassmann varieties |
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121 | (16) |
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3.4 Embedding of Grassmann spaces |
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137 | (5) |
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142 | (1) |
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4 Veronese and Segre varieties |
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143 | (80) |
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143 | (10) |
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153 | (43) |
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4.2.1 Characterisations of V2n of the first kind |
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153 | (10) |
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4.2.2 Characterisations of V2n of the second kind |
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163 | (17) |
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4.2.3 Characterisations of V2n of the third kind |
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180 | (1) |
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4.2.4 Characterisations of V2n of the fourth kind |
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181 | (15) |
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4.3 Hermitian Veroneseans |
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196 | (2) |
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4.4 Characterisations of Hermitian Veroneseans |
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198 | (3) |
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4.4.1 Characterisations of Hn,n2+2n of the first kind |
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198 | (1) |
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4.4.2 Characterisation of Hn,n2+2n of the third kind |
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199 | (1) |
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4.4.3 Characterisation of H2,8 of the fourth kind |
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200 | (1) |
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201 | (11) |
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4.6 Regular n-spreads and Segre varieties s1;n |
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212 | (7) |
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4.6.1 Construction method for n-spreads of PG(2n + 1, q) |
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219 | (1) |
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219 | (4) |
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223 | (82) |
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223 | (3) |
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5.2 Generalised quadrangles |
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226 | (6) |
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5.3 Embedded Shult spaces |
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232 | (15) |
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5.4 Lax and polarised embeddings of Shult spaces |
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247 | (6) |
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5.5 Characterisations of the classical generalised quadrangles |
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253 | (13) |
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266 | (3) |
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5.7 Embedded partial geometries |
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269 | (3) |
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5.8 (0, α)-geometries and semi-partial geometries |
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272 | (9) |
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5.9 Embedded (0, α)-geometries and semi-partial geometries |
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281 | (18) |
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5.10 Notes and references |
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299 | (6) |
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305 | (58) |
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305 | (2) |
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307 | (7) |
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6.3 The maximum size of a cap for q odd |
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314 | (5) |
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6.4 The maximum size of a cap for q even |
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319 | (6) |
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6.5 General properties of k-arcs and normal rational curves |
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325 | (7) |
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6.6 The maximum size of an arc and the characterisation of such arcs |
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332 | (6) |
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6.7 Arcs and hypersurfaces |
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338 | (22) |
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360 | (3) |
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7 Ovoids, spreads and m-systems of finite classical polar spaces |
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363 | (24) |
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7.1 Finite classical polar spaces |
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363 | (1) |
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7.2 Ovoids and spreads of finite classical polar spaces |
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364 | (1) |
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365 | (1) |
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365 | (1) |
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366 | (1) |
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7.6 m-systems and partial m-systems of finite classical polar spaces |
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367 | (1) |
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7.7 Intersections with hyperplanes and generators |
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368 | (1) |
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7.8 Bounds on partial m-systems and non-existence of m-systems |
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369 | (3) |
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7.9 m'-systems arising from a given m-system |
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372 | (2) |
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7.10 m-systems, strongly regular graphs and linear projective two-weight codes |
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374 | (2) |
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7.11 m-systems and maximal arcs |
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376 | (2) |
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7.12 Partial m-systems, BLT-sets and sets with the BLT-property |
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378 | (2) |
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7.13 m-systems and SPG-reguli |
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380 | (2) |
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382 | (1) |
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7.15 Notes and references |
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383 | (4) |
References |
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387 | (18) |
Index |
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405 | |