There 160,6504 17 160,839417 are 3 7 dim't planes in cubic a hypersurface joint with Tom Bachmann R field fi fjE Rf Xo Xn homogeneous X CD fi 03 intersection complete is Bf EXEIPE in X r plane An REE field extasio Grcr n Wendi've dim W Vectorspace S Gr tautological bundle rin Sang W Polynomials of Symds W any degree d on
g deg fi di e P symdiS Fi Tf determines fit w Te CW by c PCV ra i.IO symdis V r planes in X Scheme of Fr X 5 0 film because PWC 0 x Hi Fry Debarre Manivel For general fi of dim 8 smooth expected is
r planes how many 8 OI 0 when in X are A R Euler class eCV r ECU Eros degpr off PE Gr are isolated s.tn TCP 0 zeros r planes E y in X off Pear are simple TCP 0 it preserves orientation V R R orientable is when
e CV Ja sign Pe Gr CIR M o J READ r planes E over IR Jae F detloff in weighted count Morel Voevodsky 98J A homotopy theory Euler Kass W class Morel Morel Barge CFasel DEglise Jin Khan Raksit Hopkins M Levine Serre
and V rank V is din X when oriented relatively Gwen eCV c formal differences of GW group ring non degenerate of symmetric forms bilinear aeRY µ p presentation generators La i a field over K Kirk Las City taxy relations Lab La Lb 1 LabcatD L atb Sb a In La L tea D th GW CR 2417 13 EI 022
EZEK GWAR GWCQ EI 2 Et 2x Fp Fpt 2 Crank disc GWCFp E EI transfers separable finite k 1 field extension 3GWCKJ TrL1kiGWCLJ xv BsDi sCVxVEL59grefiT.Y.Lam Introduction to An
planese Backtocountingr Gr 1,317 eCSym3s 121 17 Kass W 15217 R field Gr Ct dtd M Levine Sym'd s e 2d D cand D ee si 241747 d l Gd 1 Cad 3 al char k t 2 lad h k field Ee ecvca is S Mckean T ec Ph ocnj Cistus S Pauli Symds e Gru 3 via dynamic intersections D 3 or Charkt 2d
a ring Let 12 be W Thin Bachmann with HER Let symdis Germy be dinV relatively oriented with dimbrcr.nl drain dir mod 2 EO c nel ice Ee l din Cn r rel Then ectzek zptee eke.ly ecvj where Vca e VCR ee en e X complete int Cory is a generic Trrepyn LJactCp I r planes P T in X
ee zeir zptee ER.GR f These are not CDs and L D's EI Kharlamov Finashin cubic surface dime a 7 3 on planes 321,489 eco ER 189 Grc 3,81 e Sym S 160,83947 1160,650C D
result with Proven integrality Thin 3 Let proper over 2C'T sm and be da orientee Vector bundle onX with rkV Lef V be a dimX rel Then e 2K 17,67 Xd JC GWCk V e d 2 If either then n eerie a natzke no hit s i 217 t Alternative perspective X vector bundle Dr 14kV 03 xx 5 Eon L I 1T How
Gwck I Tir pLJacT7 degit q ecus Morel Il joint with 1547 122 17 Kass M Levine J Solomon EI Serre Bayer Fluckiger cubic surface lines on a from IT A7X thx h Trps t 4 17 427 Cz h cx 1 2 27 747 cubic surface depends on
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