From 170f117a346015995fb5451eed223656e3c4f76c Mon Sep 17 00:00:00 2001 From: Sixto Date: Wed, 11 Jun 2025 16:40:37 +0200 Subject: [PATCH] Cambio de la cita de Faenzi. --- TFG_Sixto_José_Martínez_Gan.pdf | Bin 580226 -> 580309 bytes TFG_Sixto_José_Martínez_Gan.tex | 2 ++ bibliografia.bib | 20 ++++++++++++-------- 3 files changed, 14 insertions(+), 8 deletions(-) diff --git a/TFG_Sixto_José_Martínez_Gan.pdf b/TFG_Sixto_José_Martínez_Gan.pdf index 884e2ae09ff9e7530710b600581181014fb7d978..e36398add33a9d7a49747610c84fe52150aa0156 100644 GIT binary patch delta 33746 zcmV(h&Pz4X)>SpYulF81+Z1*g$Nlt$NADUWaWSFeB4S(IsE ztdY_FJ~FAWMG+N7iQJaazK(v2KPIw>o9WayL-PCnm#g>tD+&5(BxiAD1lXzif2*em ztY1g|h^thn(&o{h5yJ5K;6H=^4i>bvqL6vClcFf}cTGGknrXDlL@F)nNC6oCt>;xA zZS8$n>(A=s*v%pfyCMgPXYYb8t<;MTuMZFRKfZe-qlbwXm7@hJfyTKvnb5h;3-p&J z=vJm6bqW@_C{hKX1Gaksb_fOJ#Iq_jzCuL z1M|L9-Ty1{UsdF7C`Y)9=s=m_C{$kls~a7f*=#CTxxjQ3NZ;%D#Hlc)e@P_*;XZu?*i=mZXyUDA=pF7>j@C73Jtsvxh9%pqMzog6_^%^Kf6u!#c3!!7L8Oh) znmg>LTZvVd7{4*_*zN)~A?loi-Vz@eos}|vKhW5C$~Uw)&%(Tas$1_#(~lG3eB1hoN)! zTbVh=V0$heEUK|j6!UKIVG}ygY{+x?(2ZV~P1)FW52wLRe_J;wk8n^;P4m>T2X(`e z6c~#y*N&tv#kvqummzSN)r_144hZM4jLCRlAYqQR(5An%69H4(w;fS>3TArNnY_U~ zjXik*0Ha7vS^!gZ%x5rpUH6Iw*%Pch{78cPkP$xzuyb=H;J;@;8u!~98E z1rMV)0VCaLe`Mp(3{}f04@&}J@p-M7b8TCaSTuuuC@@X#+|&q~-i+M|?_gJ6xG!I&v!@X%M>Wn%+$pnpDe8wT8nQe@~SHo}so&k6$wV1nqkB-3f8uUHUvTU5nHKbo_Mvr?pyjXl zpBS8Sp}x1uWZkjtM!esacypOUhgNI18)9`r7!=vG6 z@W#yFXHUAn0WN~B&4d3^hyPLmhyPLnhyPLoxBpTE{uKi>GB}fA1So&KSxa- zZnW6!YQ|qt2L_v65<6%+40GbMmbI*wpRSI#Z;) zypUR#*&k=G2Pq(e&p3ah1uMJ=E-7PbmK#R7RYAo0tHtk`W28K4{@9s3JI^^|j65$h zDae<4k>$cUa+GO8u~?AfHWPyUc@R2Yx7VxCep2^+Q-#*s(Db}rl}%{*?H{MtRY`Fz z*qGA7@#dR zOw4k)2d%@%MYYbjAy*kFo2)ZI%EhMaQF(@uvrKVPWrCAG`z|!qsAI#)o3h7)URTSq zujd^Ny{9*Dd|rRRs4G+v$o9?0*X8mc%oB|3yQ4a4g_U0QT2iG3t-Jy;mYm`t$g?b$ zlDtiwT!2klvz_!btX5c;%Utpz=f(<_o78%RftkZ{&tVBee)Hc~$xAa-fR2ZScCDP- zox!2U57C@ZG(Nc zt9Drfn|MrdZKyJCSFxjYK_`9Pu98fk9d$~kuk4;tX{z*KfM`o#N?*Tz^`_Ltd!(CH z9qi_FLl@PTSx8&BMsOB z=mV{4-gcq-+E*9#G7P^BKd-BD75amRXc}-a%ySL2!ELkC5|~zyHjJM~^69HsXyf!i z&=z?)E*N|Yk|XjMTxz-QKp>}K+%K!ANz3B`sCKa6_sE>pYC$8t8V$6{cj)!FhJ$G` z_i}$NvSuv3%QX1R#_!aUWgA*Am}UY#Jjp>!QLY9X06%O-v*6-z;z4M-xsZxqb#XBP z?2rqgWQqy7)YLMaV&3pgGA}P68jxe=g>~TGi`)wR?*m>~nJdMLIwx)hG#l1#M)ECwQ zB|2ahy{mt(#6V3C>rWOicdr|RtF=?n=P!{vs!g>gethYp5J~zRNynEkh>^fZ!%Tmy zGNc{fT4D2bprp|A?t)3xWsU%~q$5YbgEYgf9tBBT{~Cn6TJ_%Jw2RHW_uPbIdXUQE?CLE*!4?zd7O6n#dCj_4EG#F()#Bx4h8@d%sGv_gD)V)8UNJ*bI!kB z;Oj9rj6j$TU4fr`pT9-{5f7U>;AzN+3h;5Fm55laM65mtx582<^gg(84bQ(~_rY*} z+#a__JdL#-gmDNTe+>xx7W|xt82+5JzJ2wr4fXe#fH3Rh$GTj#d+>#}I@o{9@x1^G zUw0@eg&}O8V#qh9-K=r6aB377!F>~+e4hylRR33~fp8TuI7JOgy+h6RiKYM-dcttS zTS`K_@eB%mn;pK-AfP{-1~9$w)3dr+r$P-jM{GuA?M;r5`8|1``2 zUrj*gJm{Q<)b<-d=RC435-oox9(XqPd*Hb(VG27k_`BF4@j{DmGsH3@Vi$inG7tt( zEcRl}6%?Gz#J8PP^Zrfyeou@I?{mF1(EntG+?G$uWfDak;xQ+Os11d0)|rGieitUT z5w>r@M>X3QD-v0X z5VsWI!(nebH}E#&_`-$JU-6|XK+neFi_ntKKBXZE%u8Co1?MaNhKz>rU}Nabb08+L zHoYgKQHcN1#hFLK4MNsp8dt(;V0+wqH}2sCWe+!~QC}P2HjMJ&qzM)h{oK$8r}V!7 zCO9+qJ&_iX{w?2qS}A|SMZg`?LWh!j5P=5Mk7h3b8OSb*DFDmWRT_M!+sql75RxJU z@Gv+DJaDt@E;@TeJO_YM#mFyv@p4a&Pzv*y&`tAH=q7gog$)xxVN-~hWdcyxnn?R$ z^A2_-pJE4xfTI#AW6n7cg;0~c%6DT(voVIWbUIgiFl4m)IWB(-UfH{0V#oy|L})S> z7~e}^=h5ddreZFT{YWlQfl3AJWs(bwsg$&_|B9aGHskPC`BdX$AM8I)prMNCn6v8& zb7f#Sx1q7U48Ki#Dg2F4#G}El&-7Oz+x{Xmu*LbN z>2G%jozClOHLpSi(=}Z+pVt@C$oQ89KiZe|5%7Mpcj1??RNRTFRuv7kMce`}9NXrB zpm~%Bf|@WIet9x7)DRkI{)1Vd;ng`LU?N$A=`sgfOD%t`3MlHIl@O7IoH#D)9hdbk zYxv^rlIo`I>b_my`X=hXi)K`*`}wH0fv-b%#f2b!`}wvVI)T>5BR}1Ym#XINdeMzq zWMLGpZytno4#BBXleYm{!I!$LV-|DK#yl>N9o#h&8jax|1K^WYObHF6nmm6uXd=m3q4V83gCO7&0@2rxFq^&!SZ&u`Iz}~?8Z+E4$S3|eH%DIy!p%rH zCR4ohl*8lT>f|^ig*m8@lnF|hcV|<7uL&x^RWT+0uE!@RnSbsmc+zV+Z=1~$p1<37 zh%|SpWHmVK&BG6jf*Luj^gV{br33$GaD7g>jq44{VrSGZXHWhMU9IL#m!V_?69P9k zmk|yK6t_Ea1oVFaIhPR*2o$$O@&sIs0Wr6se+ACKOEetoHt#|Bi||Eplv~;Ds5IcuVfjs!+G+v)iZpc(Pv< zbv5S&%G_!CYA?3?+^k!BsrK?1sp5U9T(;N2iDEn(Z2U#$f4{G1;c^`ySgX>eDx49U znO`gMovq|Bi=ux+;Sb6kcrbtD7fmmuT>G*Y>x?z)`g(^uL`Jo}+{U_MaCZX8Z9MM` zfpre~B5E`uZad%7+vrqEi!V1pB)10+Y6KIaqs^GW$S*L$xX-94&Jwoob>ZDE73-tq zGpdOVuf|yUe|f-sQl9K%PK$1Xn>SoC+>yTE5ch=!yu|+(wmobF`!2Xki3dW$BLRa`LVZOGVxOz;TMQ8FTY)J#+(M}syfMQ4UsN7$oqiASzqq=J zsR&vo%Zte6`dmmPh*x9vCi&9-P;>;D)gYf`7ni>4e;tYZPoFb}QOVn}kS(bspz?dd z{%w=iB>vkiJ+S?P9!^){{$?~P-E%#nHUEGtpywmF^iS6KldGWxLc|FOG16a{!S_6rfF=G`eM?pN4g}nZ{c$r3 z41Y;_e-hF1wC=a<%e%<

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z?9wv!YuP-Q4~?(@7FzMayYy6SL$g(|*wXXQD#kW6({F16cD~tiSOIJ{G8Wowf3>9_ zn$j6;QnOZA2kU{=Hfw`2bO0OIY%_EL`_pW#rFXuqtFW?W+ko82+JSv%)(Km9<9bbp zXz4W_h9l4m`rsaeJ~$31;3V|JDd2xVrf;p@_-SCevon_7)2wG1w)9r3S|e6*?;~oB zTH#~&sdd&0_g+xzoE2VqTCFiFe;)N}ja%{DYPBY;_|dPZHEG4ib#5M6>4nC~ikCmF zu37Ovx73QQR9&rBVx{gzwNfjczo}M*l|G?c<^?N#=FxDKivxlCD+6D6D)7ajz?a?# zeEG4!SMLlw{8r%WmjjPI6L>Og7E9l34SefL;M<=JJl7R?{HVV6jYbmqmRKj=r3L<#3T(r^;N1dNeyC1AcYDj jK+#H9+rq)uYNG!EvVLy;m#o?d9||xwGYTaoMNdWwN&O-w diff --git a/TFG_Sixto_José_Martínez_Gan.tex b/TFG_Sixto_José_Martínez_Gan.tex index 03ee3ba..99006a3 100644 --- a/TFG_Sixto_José_Martínez_Gan.tex +++ b/TFG_Sixto_José_Martínez_Gan.tex @@ -263,6 +263,8 @@ urlcolor=black]{hyperref} \chapter{Resumen} \todo{Configuraciones de hiperplanos, justificar. Conjetura de Terao.} + + El presente trabajo se enmarca dentro del contexto de la Conjetura de Terao para configuraciones de hiperplanos. En este trabajo estudiaremos varios aspectos del módulo de derivaciones polinómicas de un polinomio. Comenzamos dando las pinceladas básicas de la teoría de módulos para comprender con qué tipo de objeto estamos trabajando. A continuación, exploramos algunas de las dificultades que presenta este tipo de objeto con respecto a otros similares como son el espacio vectorial, en particular la determinación de la pertenencia a este y la existencia de una base. Solucionamos el primero de estos problemas introduciendo dos herramientas fundamentales de esta teoría: las bases de \Groebner{} y las sicigias. Por último, para solucionar el segundo problema, damos una detallada demostración del Criterio de Saito, un resultado que nos caracteriza para qué módulos existe una base. \selectlanguage{english} diff --git a/bibliografia.bib b/bibliografia.bib index 17b0b70..0251ece 100644 --- a/bibliografia.bib +++ b/bibliografia.bib @@ -65,15 +65,19 @@ url = {https://repository.dl.itc.u-tokyo.ac.jp/records/39646}, urldate = {2025-05-28} } -@misc{VALLES, +@article {VALLES, shorthand = {Faenzi}, - title={Saito criterion and its avatars}, - author={Daniele Faenzi and Marcos Jardim and Jean Vallès}, - year={2024}, - eprint={2402.08305}, - archivePrefix={arXiv}, - primaryClass={math.AG}, - url={https://arxiv.org/abs/2402.08305}, + AUTHOR = {Faenzi, Daniele and Jardim, Marcos and Vall\`es, Jean}, + TITLE = {Saito criterion and its avatars}, + JOURNAL = {Rend. Circ. Mat. Palermo (2)}, + FJOURNAL = {Rendiconti del Circolo Matematico di Palermo. Second Series}, + VOLUME = {73}, + YEAR = {2024}, + NUMBER = {6}, + PAGES = {2233--2243}, + ISSN = {0009-725X,1973-4409}, + DOI = {10.1007/s12215-024-01061-z}, + URL = {https://doi.org/10.1007/s12215-024-01061-z}, } @online{STACKS, shorthand = {Stacks},