Publications and preprints of Lev Borisov

Publications and preprints of Lev Borisov

Files below are in PDF format. Most of these files are posted on arxiv.org. There may be some difference in the printed versions.

  • On Hilbert modular threefolds of discriminant 49, with P.E. Gunnells, arXiv:1108.1820.
  • On CY-LG correspondence for (0,2) toric models, with R.M. Kaufmann, arXiv:1102.5444.
  • On the better behaved version of the GKZ hypergeometric system, with R.P. Horja, arXiv:1011.5720.
  • Berglund-Hubsch mirror symmetry via vertex algebras, arXiv:1007.2633.
  • Finding integral diagonal pairs in a two dimensional N-set, with R. Jin, arXiv:1007.1441.
  • Twistor geometry and warped product orthogonal complex structures, with S. Salamon and J. Viaclovsky, to appear in Duke Math. J.
  • Absorption Probabilities for the Two-Barrier Quantum Walk, with E. Bach, preprint arXiv:0901.4349.
  • Threefolds of order one in the six-quadric, with J. Viaclovsky, Proceedings of the Steklov Institute of Mathematics, 264 (2009), 18--29.
  • On the conjecture of King for smooth toric Deligne-Mumford stacks, with Z. Hua, Adv. Math. 221 (2009), no. 1, 277--301.
  • On Calabi-Yau threefolds with large nonabelian fundamental groups, with Z. Hua, Proc. Amer. Math. Soc. 136 (2008), no. 5, 1549--1551.
  • The Pfaffian-Grassmannian derived equivalence, with A. Caldararu, J. Algebraic Geom. 18 (2009), no. 2, 201--222.
  • Higher elliptic genera, with A. Libgober, Math. Res. Lett. 15 (2008), no. 3, 511--520.
  • Mellin-Barnes integrals as Fourier-Mukai transforms, with R.P. Horja, Adv. Math. 207 (2006), no. 2, 876--927.
  • On the $K$-theory of smooth toric DM stacks, with R.P. Horja, Snowbird lectures on string geometry, 21--42, Contemp. Math., 401, Amer. Math. Soc., Providence, RI, 2006.
  • On Wronskians of weight one Eisenstein series, J. Number Theory 121 (2006), no. 1, 132--152.
  • Holomorphic Eisenstein series with Jacobian twists, Algebraic geometry, 1--15, Contemp. Math., 422, Amer. Math. Soc., Providence, RI, 2007.
  • McKay correspondence for elliptic genera, with A. Libgober, Ann. of Math. (2) 161 (2005), no. 3, 1521--1569.
  • The Orbifold Chow ring of a toric Deligne-Mumford stack, with L. Chen and G. Smith, J. Amer. Math. Soc. 18 (2005), no. 1, 193--215.
  • Self-self-dual spaces of polynomials, with E. Mukhin, Adv. Math. 190 (2005), no. 1, 77--118.
  • Higher Stanley-Reisner rings and Toric Residues, Compos. Math. 141 (2005), no. 1, 161--174.
  • Chiral rings of vertex algebras of mirror symmetry, Math. Z. 248 (2004), no. 3, 567--591.
  • String cohomology of Calabi-Yau hypersurfaces via Mirror Symmetry, with A.R. Mavlyutov, Adv. Math. 180 (2003), no. 1, 355--390.
  • Toric modular forms of higher weight, with P.E. Gunnells, J. Reine Angew. Math. 560 (2003), 43--64.
  • Wonderful blowups associated to group actions, with P.E. Gunnells, Selecta Math. (N.S.) 8 (2002), no. 3, 373--379.
  • Elliptic Genera of singular varieties, orbifold elliptic genus and chiral deRham complex, with A. Libgober, Mirror symmetry, IV (Montreal, QC, 2000), 325--342, AMS/IP Stud. Adv. Math., 33, Amer. Math. Soc., Providence, RI, 2002.
  • Elliptic Genera of Singular Varieties, with A. Libgober, Duke Math. J. 116 (2003), no. 2, 319--351.
  • Elliptic functions and equations of modular curves, with P. E. Gunnells and S. Popescu, Math. Ann. 321 (2001), 553-568.
  • Toric modular forms and nonvanishing of L-functions, with P. E. Gunnells, J. Reine Angew. Math. 539 (2001), 149--165.
  • Toric Varieties and Modular Forms, with P. E. Gunnells, Invent. Math. 144 (2001), no. 2, 297--325.
  • Introduction to the vertex algebra approach to mirror symmetry, preprint math.AG/9912195.
  • Vertex algebras and mirror symmetry, Comm. Math. Phys. 215 (2001), no. 3, 517--557.
  • Elliptic genera of toric varieties and applications to mirror symmetry, with A. Libgober, Invent. Math. 140 (2000), no. 2, 453--485.
  • String cohomology of a toroidal singularity, J. Algebraic Geom. 9 (2000), no. 2, 289--300.
  • A finiteness theorem for subgroups of Sp(4,Z), Algebraic geometry, 9. J. Math. Sci. (New York) 94 (1999), no. 1, 1073--1099.
  • Systematic approach to cyclic orbifolds, with M. B. Halpern and C. Schweigert, Internat. J. Modern Phys. A 13 (1998), no. 1, 125--168.
  • Mirror duality and string-theoretic Hodge numbers, with V. V. Batyrev, Invent. Math. 126 (1996), no. 1, 183--203.
  • On Calabi-Yau complete intersections in toric varieties, with V. V. Batyrev, Higher-dimensional complex varieties (Trento, 1994), 39--65, de Gruyter, Berlin, 1996.
  • Dual cones and mirror symmetry for generalized Calabi-Yau manifolds, with V. V. Batyrev, Mirror symmetry, II, 71--86, AMS/IP Stud. Adv. Math., 1, Amer. Math. Soc., Providence, RI, 1997.
  • Towards the Mirror Symmetry for Calabi-Yau complete intersections in Gorenstein Toric Fano Varieties, preprint math.AG/9310001.
  • Singular toric Fano three-folds, with A. A. Borisov, Russian Acad. Sci. Sb. Math. 75 (1993), no. 1, 277--283.