A note on higher-order Gauss maps

Michigan Mathematical Journal - Tập 66 Số 1 - 2017
Sandra Di Rocco1,2, Kelly Jabbusch1,2, Anders Lundman1,2
1Department of Mathematics & Statistics University of Michigan-Dearborn 4901 Evergreen Road Dearborn, MI 48128-2406 USA
2Department of Mathematics Royal Institute of Technology (KTH) 10044 Stockholm Sweden

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Tài liệu tham khảo

D. A. Cox, J. B. Little, and H. K. Schenck, <i>Toric varieties</i>, Grad. Stud. Math., 124, American Mathematical Society, Providence, RI, 2011.

A. Atanasov, C. Lopez, A. Perry, N. Proudfoot, and M. Thaddeus, <i>Resolving toric varieties with Nash blowups</i>, Exp. Math. 20 (2011), no. 3, 288–303, http://dx.doi.org/10.1080/10586458.2011.565238.

T. Bauer, S. Di Rocco, and T. Szemberg, <i>Generation of jets on K3 surfaces</i>, J. Pure Appl. Algebra 146 (2000), no. 1, 17–27.

T. Bauer and T. Szemberg, <i>Higher order embeddings of Abelian varieties</i>, Math. Z. 224 (1997), no. 3, 449–455, http://dx.doi.org/10.1007/PL00004591.

M. C. Beltrametti, S. Di Rocco, and A. J. Sommese, <i>On higher order embeddings of Fano threefolds by the anticanonical linear system</i>, J. Math. Sci. Univ. Tokyo 5 (1998), no. 1, 75–97.

M. C. Beltrametti and A. J. Sommese, <i>On $k$</i>-jet ampleness, Complex analysis and geometry, Univ. Ser. Math., pp. 355–376, Plenum, New York, 1993.

M. C. Beltrametti and A. J. Sommese, <i>The adjunction theory of complex projective varieties</i>, de Gruyter Exp. Math., 16, Walter de Gruyter &amp; Co., Berlin, 1995, http://dx.doi.org/10.1515/9783110871746.

M. Castellani, <i>Sule superfici i cui spazi osculatori sono biosculatori</i>, Rom. Acc. I. Rend. 5 (1922), no. 31, 347–350.

K. Cho, Y. Miyaoka, and N. I. Shepherd-Barron, <i>Characterizations of projective space and applications to complex symplectic manifolds</i>, Higher dimensional birational geometry (Kyoto, 1997), Adv. Stud. Pure Math., 35, pp. 1–88, Math. Soc. Japan, Tokyo, 2002.

P. De Poi and G. Ilardi, <i>On higher Gauss maps</i>, J. Pure Appl. Algebra 219 (2015), no. 11, 5137–5148, http://www.sciencedirect.com/science/article/pii/S0022404915001243.

S. Di Rocco, <i>Generation of $k$-jets on toric varieties</i>, Math. Z. 231 (1999), no. 1, 169–188.

S. Di Rocco and A. J. Sommese, <i>Line bundles for which a projectivized jet bundle is a product</i>, Proc. Amer. Math. Soc. 129 (2001), no. 6, 1659–1663, http://dx.doi.org/10.1090/S0002-9939-00-05875-5.

D. Franco and G. Ilardi, <i>On multiosculating spaces</i>, Comm. Algebra 29 (2001), 2961–2976.

W. Fulton, <i>Introduction to toric varieties</i>, Ann. of Math. Stud., 131, Princeton University Press, Princeton, NJ, 1993.

W. Fulton, S. Kleiman, R. Piene, and H. Tai, <i>Some intrinsic and extrinsic characterizations of the projective space</i>, Bull. Soc. Math. France 113 (1985), no. 2, 205–210, http://www.numdam.org/item?id=BSMF_1985__113__205_0.

K. Furukawa and A. Ito, <i>Gauss maps of toric varieties</i>, 2014, arXiv: 1403.0793.

D. R. Grayson and M. Stillman, <i>Macaulay2, a software system for research in algebraic geometry</i>, http://www.math.illinois.edu/Macaulay2/.

P. Griffiths and J. Harris, <i>Algebraic geometry and local differential geometry</i>, Ann. Sci. Éc. Norm. Supér. (4) 12 (1979), no. 3, 355–452, http://www.numdam.org/item?id=ASENS_1979_4_12_3_355_0.

M. M. Kapranov, <i>A characterization of $A$</i>-discriminantal hypersurfaces in terms of the logarithmic Gauss map, Math. Ann. 290 (1991), no. 2, 277–285, http://dx.doi.org/10.1007/BF01459245.

S. Kleiman and R. Piene, <i>On the inseparability of the Gauss map</i>, Enumerative algebraic geometry (Copenhagen, 1989), Contemp. Math., 123, pp. 107–129, Amer. Math. Soc., Providence, RI, 1991, http://dx.doi.org/10.1090/conm/123/1143550.

J. M. Landsberg, <i>On second fundamental forms of projective varieties</i>, Invent. Math. 117 (1994), no. 1, 303–315, http://dx.doi.org/10.1007/BF01232243.

A. Lanteri and R. Mallavibarrena, <i>Osculatory behavior and second dual varieties of del Pezzo surfaces</i>, Adv. Geom. 1 (2001), no. 4, 345–363.

A. Lundman and G. S. dén Stå hl, <i>LatticePolytopes, a package for computations with Lattice Polytopes</i>, http://www.math.illinois.edu/Macaulay2/.

D. Perkinson, <i>Inflections of toric varieties</i>, Michigan Math. J. 48 (2000), 483–515, http://dx.doi.org/10.1307/mmj/1030132730.

R. Piene, <i>A note on higher order dual varieties, with an application to scrolls</i>, Singularities, Part 2 (Arcata, Calif., 1981), Proc. Sympos. Pure Math., 40, pp. 335–342, Amer. Math. Soc., Providence, RI, 1983.

W. Pohl, <i>Differential geometry of higher order</i>, Topology 1 (1962), 169–211.

H. Terakawa, <i>Higher order embeddings of algebraic surfaces of Kodaira dimension zero</i>, Math. Z. 229 (1998), no. 3, 417–433.

F. L. Zak, <i>Tangents and secants of algebraic varieties</i>, Transl. Math. Monogr., 127, American Mathematical Society, Providence, RI, 1993, translated from the Russian manuscript by the author.