UNIVERSAL CALABI-YAU ALGEBRA: TOWARDS AN UNIFICATION OF GEOMETRY WITH SU(N) HOLONOMY

Anselmo F., Maslikov A., Volkov G. Universal Calabi-Yau Algebra: Towards an Unification of Geometry with SU(n) Holonomy: IHEP Preprint 2002–39. – Protvino, 2002. – p. 22, figs. 9, tables 3, refs.: 12. We discuss some results in Calabi-Yau universal-gebra suitable for constructing and classifying the infinite series of the compact complex spaces with SU(n) holonomy. This universal-gebraic approach includes natural extensions of reflexive weight vectors to higher dimensions. It includes a ‘dual’ construction based on the Diophantine decomposition of invariant monomials, which provides explicit recurrence formulae for the numbers of Calabi-Yau spaces in arbitrary dimensions. aNNOTACIQ aNSELXMO f., mASLIKOW a., wOLKOW g. uNIWERSALXNAQ kALABI–qU ALGEBRA: K EDINOJ GEOMETRII S SU(n) GOLONOMIEJ: pREPRINT ifw— 2002–39. – pROTWINO, 2002. – 22 S., 9 RIS., 3 TABL., BIBLIOGR.: 12. mY OBSUVDAEM NEKOTORYE REZULXTATY W OBLASTI kALABI-qU UNIWERSALGEBRY, KOTORYE MOGUT BYTX ISPOLXZOWANY DLQ POSTROENIQ I KLASSIFIKACII BESKONEˆNYH SERIJ KOMPAKTNYH KOMPLEKSNYH PROSTRANSTW S SU(n) GOLONOMIEJ. nA[ UNIWERSALGEBRAIˆESKIJ PODHOD WKL@ˆAET ESTESTWENNYE RAS[IRENIQ REFLEKSIWNYH WESOWYH WEKTOROW W WYS[IH RAZMERNOSTQH. —TO WKL@ˆAET DUALXNU@ KONSTRUKCI@, OSNOWANNU@ NA dIOFANTOWOM RAZLOVENII INWARIANTNYH MONOMOW, ˆTO DAET QWNYE REKURENTNYE FORMULY DLQ MNOVESTW PROSTRANSTW kALABI-qU W PROIZWOLXNOJ RAZMERNOSTI. c © State Research Center of Russia Institute for High Energy Physics, 2002 Dedicated to the memories of Maria Volkova and Julia Fadeeva