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Rational normal scroll

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161: 66: 25: 310: > 0. Choose rational normal curves in these two linear subspaces, and choose an isomorphism φ between them. Then the rational normal surface consists of all lines joining the points 190: 76: 38: 376: 263: + 1. Here "rational" means birational to projective space, "scroll" is an old term for ruled surface, and "normal" refers to 134: 230: 212: 52: 106: 113: 91: 120: 173: 402: 44: 183: 177: 169: 360: 102: 194: 368: 264: 127: 372: 356: 283: 256: 386: 382: 83: 396: 268: 248: 330:
is 0, the rational normal scroll becomes a cone over a rational normal curve. If
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is uniquely determined by the rational normal scroll and is called the
302: + 1 choose two complementary linear subspaces of dimensions 154: 59: 18: 87: 182:but its sources remain unclear because it lacks 274:A non-degenerate irreducible surface of degree 8: 92:introducing citations to additional sources 53:Learn how and when to remove these messages 282:is either a rational normal scroll or the 338:then the rational normal curve of degree 231:Learn how and when to remove this message 213:Learn how and when to remove this message 82:Relevant discussion may be found on the 322:). In the degenerate case when one of 7: 367:, Wiley Classics Library, New York: 14: 294:In projective space of dimension 34:This article has multiple issues. 365:Principles of algebraic geometry 159: 75:relies largely or entirely on a 64: 23: 42:or discuss these issues on the 1: 419: 168:This article includes a 103:"Rational normal scroll" 197:more precise citations. 306: > 0 and 245:rational normal scroll 369:John Wiley & Sons 265:projective normality 88:improve this article 403:Algebraic geometry 357:Griffiths, Phillip 278: – 1 in 243:In mathematics, a 170:list of references 16:Algebraic geometry 378:978-0-471-05059-9 241: 240: 233: 223: 222: 215: 153: 152: 138: 57: 410: 389: 334: <  284:Veronese surface 257:projective space 236: 229: 218: 211: 207: 204: 198: 193:this article by 184:inline citations 163: 162: 155: 148: 145: 139: 137: 96: 68: 60: 49: 27: 26: 19: 418: 417: 413: 412: 411: 409: 408: 407: 393: 392: 379: 355: 352: 346:of the scroll. 292: 237: 226: 225: 224: 219: 208: 202: 199: 188: 174:related reading 164: 160: 149: 143: 140: 97: 95: 81: 69: 28: 24: 17: 12: 11: 5: 416: 414: 406: 405: 395: 394: 391: 390: 377: 361:Harris, Joseph 351: 348: 291: 288: 269:normal schemes 239: 238: 221: 220: 178:external links 167: 165: 158: 151: 150: 86:. Please help 72: 70: 63: 58: 32: 31: 29: 22: 15: 13: 10: 9: 6: 4: 3: 2: 415: 404: 401: 400: 398: 388: 384: 380: 374: 370: 366: 362: 358: 354: 353: 349: 347: 345: 341: 337: 333: 329: 325: 321: 317: 313: 309: 305: 301: 298: +  297: 289: 287: 285: 281: 277: 272: 270: 266: 262: 259:of dimension 258: 254: 250: 249:ruled surface 246: 235: 232: 217: 214: 206: 203:November 2021 196: 192: 186: 185: 179: 175: 171: 166: 157: 156: 147: 144:November 2021 136: 133: 129: 126: 122: 119: 115: 112: 108: 105: –  104: 100: 99:Find sources: 93: 89: 85: 79: 78: 77:single source 73:This article 71: 67: 62: 61: 56: 54: 47: 46: 41: 40: 35: 30: 21: 20: 364: 343: 339: 335: 331: 327: 323: 319: 315: 311: 307: 303: 299: 295: 293: 290:Construction 279: 275: 273: 260: 252: 244: 242: 227: 209: 200: 189:Please help 181: 141: 131: 124: 117: 110: 98: 74: 50: 43: 37: 36:Please help 33: 195:introducing 350:References 251:of degree 114:newspapers 39:improve it 344:directrix 84:talk page 45:talk page 397:Category 363:(1994), 387:1288523 191:improve 128:scholar 385:  375:  130:  123:  116:  109:  101:  267:(not 247:is a 176:, or 135:JSTOR 121:books 373:ISBN 314:and 271:). 107:news 326:or 255:in 90:by 399:: 383:MR 381:, 371:, 359:; 286:. 180:, 172:, 48:. 340:m 336:n 332:m 328:n 324:m 320:x 318:( 316:φ 312:x 308:n 304:m 300:n 296:m 280:P 276:m 261:n 253:n 234:) 228:( 216:) 210:( 205:) 201:( 187:. 146:) 142:( 132:· 125:· 118:· 111:· 94:. 80:. 55:) 51:(

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improve it
talk page
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single source
talk page
improve this article
introducing citations to additional sources
"Rational normal scroll"
news
newspapers
books
scholar
JSTOR
list of references
related reading
external links
inline citations
improve
introducing
Learn how and when to remove this message
Learn how and when to remove this message
ruled surface
projective space
projective normality
normal schemes
Veronese surface
Griffiths, Phillip
Harris, Joseph
John Wiley & Sons

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