u.ewhy of cohomology of complex Complete variables e da dingo e g - PDF document

Computing syzygies Juliette Bruce of algebraic varieties Where I work and live occupies the ancestral lands of the 9 Lo Chunk am giving this talk from is people less than 2 blocks and where I away from where Tony Robinson was murdered by the police Black and Indigenous Lives Matter the 51st anniversary of the start of the Stonewall Tonight tomorrow marks a pivotal moment in the fight for LGBT t equality Riot Revolution dead by Black Brown Indigenous trans women of color Flappy Pride t Lives Matter otee Black and Indigenous LGBT Fetuses mm ao_so era i X Ipr B sm proj voiety Exo x S in hang defining ideal X E IP Ix S x SII x F O C Fo Fp c Fr Sx C o min groded free res III Eis mine Brecxepr s Betti s syzygies Betti grade The syzygies embedding XElPr are extrinsic e.g depend on the Betti s

T hm Let X E IP Ein Green Lazarsfeld be a smooth curve if de 0 then i X Bp.pt X C Pr D 1 0 O E p E r g X b gonality of X f The Betti capture some ofthe intrinsic geometry of smooth curves s 2 low is the Intrinsic geometry of higher dim Varieties Centrums e g dim X 2 captured by their syzygies at s of P2 simpleton What are the syzygies Ipetti Leg next case with simplest geometry a pr IP xd xdy x y 2 1 za a L d'uple Veronesemap image veronese surf Bp z P2 d Bp z IP Ipr d uple Betti of s Veronese surface d s of R TEqbringTg Betti R Exy z Bp 2 P2 d dime Terps S x G of NBA Resolve Cos m S module via Koszal complex resolve Sx symbolically via g b methods e no s Is u.ewhy of cohomology of complex Complete variables e da dingo e g Compute theranksof matrices L sparse so

so ore FLU E HAI ad FEELEHED But the matrices we are dealing w compute the Betti of P2 for 1 E de 6 Results Bruce Erman Goldstein Yang s 0 Ebc d as well as the corresponding multi worn graded Betti similar by Greco Martino s Schur Betti s andcostryctgcooes.Demeye.lemr.cn Boi j Seidenberg Decompositions The complex respects the 23 multigreding on R Flown D differentials ore block diagonal Sparse numerical liner algebra B e.g.LU R decompositions high performance high throughput computing d hundreds thousands of computers supercomputers workingat once e g LHC Human Genome as Smee https syzygydota.com Veronese for M2 Schur Ein Erma Lazarsfeld 5 There exists an explict set ofmonomial Conjecture syzygies Ep 2 UP d such thot D CD d Bp HIP d to Epa 0 A small subset of very special syzygies is controlling non vanishing With Epa P2 d Bruce ErmanGoldsteinYong as above i Conjecture P syzygies of Ep q P2 d d w dw a deg 2 dominant Schur weights