Knowledge (XXG)

Behrend function

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333: 195: 80: 237: 374: 102: 367: 398: 360: 36: 90: 259: 201: 267: 44: 285: 255: 209: 340: 294: 20: 393: 344: 304: 258:?), the definition extends to moduli stacks such as the moduli stack of stable sheaves (the 316: 312: 387: 190:{\displaystyle \chi (X,\nu _{X})=\sum _{n\in \mathbb {Z} }n\,\chi (\{\nu _{X}=n\})} 308: 332: 280: 32: 263: 247: 299: 283:(2009), "Donaldson–Thomas type invariants via microlocal geometry", 254:. Modulo some solvable technical difficulties (e.g., what is the 348: 89:
is a quasi-projective proper moduli scheme carrying a
212: 105: 47: 231: 189: 74: 368: 8: 181: 162: 375: 361: 75:{\displaystyle \nu _{X}:X\to \mathbb {Z} } 298: 223: 211: 169: 155: 146: 145: 138: 122: 104: 68: 67: 52: 46: 7: 329: 327: 246:, which is an element of the zeroth 347:. You can help Knowledge (XXG) by 14: 331: 220: 213: 184: 159: 128: 109: 64: 16:Function in algebraic geometry 1: 232:{\displaystyle ^{\text{vir}}} 95:weighted Euler characteristic 309:10.4007/annals.2009.170.1307 91:symmetric obstruction theory 415: 326: 202:virtual fundamental class 399:Algebraic geometry stubs 260:Donaldson–Thomas theory 343:–related article is a 233: 191: 76: 37:constructible function 286:Annals of Mathematics 256:Chow group of a stack 234: 200:is the degree of the 192: 77: 268:Gromov–Witten theory 210: 103: 45: 341:algebraic geometry 229: 187: 151: 72: 21:algebraic geometry 356: 355: 226: 134: 406: 377: 370: 363: 335: 328: 319: 302: 293:(3): 1307–1338, 238: 236: 235: 230: 228: 227: 224: 196: 194: 193: 188: 174: 173: 150: 149: 127: 126: 81: 79: 78: 73: 71: 57: 56: 31:, introduced by 25:Behrend function 414: 413: 409: 408: 407: 405: 404: 403: 384: 383: 382: 381: 324: 279: 276: 219: 208: 207: 165: 118: 101: 100: 48: 43: 42: 17: 12: 11: 5: 412: 410: 402: 401: 396: 386: 385: 380: 379: 372: 365: 357: 354: 353: 336: 322: 321: 275: 272: 240: 239: 222: 218: 215: 198: 197: 186: 183: 180: 177: 172: 168: 164: 161: 158: 154: 148: 144: 141: 137: 133: 130: 125: 121: 117: 114: 111: 108: 83: 82: 70: 66: 63: 60: 55: 51: 15: 13: 10: 9: 6: 4: 3: 2: 411: 400: 397: 395: 392: 391: 389: 378: 373: 371: 366: 364: 359: 358: 352: 350: 346: 342: 337: 334: 330: 325: 318: 314: 310: 306: 301: 296: 292: 288: 287: 282: 278: 277: 273: 271: 269: 265: 262:) or that of 261: 257: 253: 249: 245: 216: 206: 205: 204: 203: 178: 175: 170: 166: 156: 152: 142: 139: 135: 131: 123: 119: 115: 112: 106: 99: 98: 97: 96: 92: 88: 85:such that if 61: 58: 53: 49: 41: 40: 39: 38: 34: 30: 26: 22: 349:expanding it 338: 323: 300:math/0507523 290: 289:, 2nd Ser., 284: 281:Behrend, Kai 251: 243: 241: 199: 94: 86: 84: 28: 27:of a scheme 24: 18: 264:stable maps 93:, then the 33:Kai Behrend 388:Categories 274:References 248:Chow group 167:ν 157:χ 143:∈ 136:∑ 120:ν 107:χ 65:→ 50:ν 394:Geometry 317:2600874 35:, is a 315:  23:, the 339:This 295:arXiv 266:(the 345:stub 305:doi 291:170 270:). 250:of 242:of 225:vir 19:In 390:: 313:MR 311:, 303:, 376:e 369:t 362:v 351:. 320:. 307:: 297:: 252:X 244:X 221:] 217:X 214:[ 185:) 182:} 179:n 176:= 171:X 163:{ 160:( 153:n 147:Z 140:n 132:= 129:) 124:X 116:, 113:X 110:( 87:X 69:Z 62:X 59:: 54:X 29:X

Index

algebraic geometry
Kai Behrend
constructible function
symmetric obstruction theory
virtual fundamental class
Chow group
Chow group of a stack
Donaldson–Thomas theory
stable maps
Gromov–Witten theory
Behrend, Kai
Annals of Mathematics
arXiv
math/0507523
doi
10.4007/annals.2009.170.1307
MR
2600874
Stub icon
algebraic geometry
stub
expanding it
v
t
e
Categories
Geometry
Algebraic geometry stubs

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