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 mirrors of elliptically fibered K3 surfaces, arXiv:1702.03919.
  • Optimality of the relaxed polar factors by a characterization of the set of real square roots of real symmetric matrices, with Andreas Fischle and Patrizio Neff, arXiv:1606.09085.
  • Ulrich Bundles on Enriques Surfaces, with Howard Nuer, arXiv:1606.01459.
  • On Clifford double mirrors of toric complete intersections, with Zhan Li, arXiv:1601.00809.
  • The sum of squared logarithms inequality in arbitrary dimensions, with Patrizio Neff, Suvrit Sra and Christian Thiel, arXiv:1508.04039.
  • Stringy $E$-functions of Pfaffian-Grassmannian double mirrors, with A. Libgober, arXiv:1502.03702.
  • Class of the affine line is a zero divisor in the Grothendieck ring, arXiv:1412.6194.
  • On complete intersections with trivial canonical class, with Zhan Li, Adv. Math. 268 (2015), 339--349.
  • Book review: "Classical Algebraic Geometry: A Modern View" by I.V. Dolgachev , to appear in Bulletin of AMS.
  • Applications of homological mirror symmetry to hypergeometric systems: duality conjectures, with R.P. Horja, arXiv:1308.2238.
  • On (2,4) complete intersection threefolds that contain an Enriques surface, with H. Nuer, arXiv:1210.1903.
  • On stringy cohomology spaces, Duke Math. J. 163 (2014), no. 6, 1105--1126.
  • On Hilbert modular threefolds of discriminant 49, with P.E. Gunnells, Selecta Math. (N.S.) 19 (2013), no. 4, 923--947.
  • On CY-LG correspondence for (0,2) toric models, with R.M. Kaufmann, Adv. Math. 230 (2012), no. 2, 531-551.
  • On the better behaved version of the GKZ hypergeometric system, with R.P. Horja, Math. Ann. 357 (2013), no. 2, 585-603.
  • Berglund-Hubsch mirror symmetry via vertex algebras, Comm. Math. Phys. 320 (2013), no. 1, 73?.
  • Finding integral diagonal pairs in a two dimensional N-set, with R. Jin, Proc. Amer. Math. Soc. 139 (2011), no. 7, 2431-2434.
  • Twistor geometry and warped product orthogonal complex structures, with S. Salamon and J. Viaclovsky, Duke Math. J. 156 (2011), no. 1, 125–166.
  • 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.