Some Preprints

Applied Mathematics

Daniel J. Bates, Jonathan D. Hauenstein, Christoper Peterson, and Andrew J. Sommese, NUMERICAL DECOMPOSITION OF THE RANK-DEFICIENCY SET OF A MATRIX OF MULTIVARIATE POLYNOMIALS (PDF file, 26 pages); postscript version; dvi version.

Daniel J. Bates, Christoper Peterson, Andrew J. Sommese, and Charles W. Wampler, NUMERICAL COMPUTATION OF THE GENUS OF AN IRREDUCIBLE CURVE WITHIN AN ALGEBRAIC SET (PDF file, 11 pages); postscript version; dvi version.

Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler, SOFTWARE FOR NUMERICAL ALGEBRAIC GEOMETRY: A PARADIGM AND PROGRESS TOWARDS ITS IMPLEMENTATION (PDF file, 16 pages); postscript version; dvi version.

Daniel J. Bates, Christoper Peterson, and Andrew J. Sommese, APPLICATIONS OF A NUMERICAL VERSION OF TERRACINI'S LEMMA FOR SECANTS AND JOINS (PDF file, 14 pages); postscript version; dvi version.

Ye Lu, Daniel J. Bates, Andrew J. Sommese, and Charles W. Wampler, FINDING ALL REAL POINTS OF A COMPLEX CURVE (PDF file, 31 pages), to appear Contemporary Mathematics.

Daniel J. Bates, Andrew J. Sommese, Jonathan D. Hauenstein, and Charles W. Wampler, ADAPTIVE MULTIPRECISION PATH TRACKING (PDF file, 31 pages); postscript version; dvi version, to appear SIAM Journal on Numerical Analysis.

Andrew J. Sommese and Charles W. Wampler, EXCEPTIONAL SETS AND FIBER PRODUCTS (PDF file, 31 pages); postscript version; dvi version, to appear Foundations of Computational Mathematics.

Daniel J. Bates, Christoper Peterson, and Andrew J. Sommese, A NUMERICAL-SYMBOLIC ALGORITHM FOR COMPUTING THE MULTIPLICITY OF A COMPONENT OF AN ALGEBRAIC SET (PDF file, 18 pages); postscript version; DVI version, Journal of Complexity 22 (2006), 475-489.

Eugene L. Allgower, Daniel J. Bates, Andrew J. Sommese, and Charles W. Wampler, SOLUTION OF POLYNOMIAL SYSTEMS DERIVED FROM DIFFERENTIAL EQUATIONS (DVI file, 13 pages); postscript version; pdf version, Computing 76 (2005), 1-10.

Andrew J. Sommese and Charles W. Wampler, NUMERICAL SOLUTION OF POLYNOMIAL SYSTEMS ARISING IN ENGINEERING AND SCIENCE, (2005), 401+xxii pages, World Scientific Press, Singapore.

Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler, SOLVING POLYNOMIAL SYSTEMS EQUATION BY EQUATION (DVI file, 21 pages); postscript version; pdf version.

Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler, AN INTRINSIC HOMOTOPY FOR INTERSECTING ALGEBRAIC VARIETIES (DVI file, 20 pages); postscript version; pdf version, Journal of Complexity 21 (2005): 593-608.

Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler, HOMOTOPIES FOR INTERSECTING SOLUTION COMPONENTS OF POLYNOMIAL SYSTEMS (DVI file, 20 pages); postscript version; pdf version, SIAM Journal on Numerical Analysis, 42 (2004), 1552-1571.

Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler, NUMERICAL FACTORIZATION OF MULTIVARIATE COMPLEX POLYNOMIALS (DVI file, 17 pages); postscript version; pdf version, Theoretical Computer Science 315 (2004), 651-669.

Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler, ADVANCES IN POLYNOMIAL CONTINUATION FOR SOLVING PROBLEMS IN KINEMATICS (postscript file, 18 pages), Paper DETC2002/MECH-34254, Proc. ASME Design Engineering Technical Conf. (CDROM), Montreal, Quebec, Sept. 29-Oct. 2, 2002. Revised version in ASME Journal of Mechanical Design 126 (2004), 262-268.

Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler, A METHOD FOR TRACKING SINGULAR PATHS WITH APPLICATION TO THE NUMERICAL IRREDUCIBLE DECOMPOSITION (DVI file, 17 pages); postscript version; pdf version;, in ``Algebraic Geometry, a Volume in Memory of Paolo Francia,'' ed. by M.C. Beltrametti, F. Catanese, C. Ciliberto, A. Lanteri, and C. Pedrini; De Gruyter (2002), 329-345.

Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler, SYMMETRIC FUNCTIONS APPLIED TO DECOMPOSING POLYNOMIAL SYSTEMS (DVI file, 21 pages); postscript version; pdf version, SIAM Journal on Numerical Analysis 40 (2002), pages 2026-2046.

Eugene L. Allgower and Andrew J. Sommese, PIECEWISE LINEAR APPROXIMATION OF SMOOTH COMPACT FIBERS (pdf file); Journal of Complexity 18 (2002), 547-556.

Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler, NUMERICAL IRREDUCIBLE DECOMPOSITION USING PHCpack (DVI file, 20 pages); postscript version; pdf version, in "Mathematics and Visualization," edited by M. Joswig and N. Takayama, Springer-Verlag (2003), 109-130.

Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler, USING MONODROMY TO DECOMPOSE SOLUTION SETS OF POLYNOMIAL SYSTEMS INTO IRREDUCIBLE COMPONENTS (DVI file, 19 pages); postscript version; pdf version, in Proceedings of the 2001 NATO Advance Research Conference, Eilat, Israel, on Applications of Algebraic Geometry to Coding Theory, Physics, and Computation, edited by C. Ciliberto, F. Hirzebruch, R. Miranda, and M. Teicher, (2001) 297-315.

Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler, NUMERICAL IRREDUCIBLE DECOMPOSITION USING PROJECTIONS FROM POINTS ON COMPONENTS (DVI file, 15 pages); postscript version; pdf version, in ``Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering,'' ed. by Green, Hosten, Laubenbacher, and Power, Contemporary Mathematics 206 (2001), pages 37-51.

Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler, NUMERICAL DECOMPOSITION OF THE SOLUTION SETS OF POLYNOMIAL SYSTEMS INTO IRREDUCIBLE COMPONENTS, SIAM Journal on Numerical Analysis 38 (2001), Number 6 2022-2046 .

Amarjit S. Budhiraja and Andrew J. Sommese, CLASSICAL INTEGRATION RULES AND WIENER MEASURE (2000) (DVI file, 19 pages); postscript version; pdf version.

Steven M. Wise, Andrew J. Sommese, and Layne T. Watson, ALGORITHM 801: POLSYS_PLP: A PARTITIONED LINEAR PRODUCT HOMOTOPY CODE FOR SOLVING POLYNOMIAL SYSTEMS OF EQUATIONS, ACM Transactions on Mathematical Software (TOMS) 26 (2000), 176-200.

Andrew J. Sommese and Jan Verschelde, NUMERICAL HOMOTOPIES TO COMPUTE GENERIC POINTS ON POSITIVE DIMENSIONAL ALGEBRAIC SETS , Journal of Complexity 16 (2000), 572-602.

Andrew J. Sommese and Charles W. Wampler, NUMERICAL ALGEBRAIC GEOMETRY(DVI file, 15 pages) postscript version; pdf; in The Mathematics of Numerical Analysis: Real Number Algorithms, Park City, Utah, Summer 1995, ed. by J. Renegar, M. Shub, and S. Smale, Lectures in Applied Math. 32 (1996), 749-763.

Alexander P. Morgan, Andrew J. Sommese and Charles W. Wampler, A PRODUCT-DECOMPOSITION BOUND FOR BEZOUT NUMBERS, SIAM Journal on Numerical Analysis 32 (1995), 1308-1325.

Alexander P. Morgan, Andrew J. Sommese and Layne T. Watson, FINDING ALL SOLUTIONS TO POLYNOMIAL SYSTEMS USING HOMPACK, ACM Transactions on Mathematical Software 15 (1989), 93-122.

Pure Mathematics

M.C. Beltrametti, C. Ciliberto, A. Lanteri, and A.J. Sommese, ON THE BIRATIONALITY OF THE BICANONICAL MAP OF A SURFACE SECTION OF A THREEFOLD (DVI file, 25 pages); postscript version; pdf version, to appear Communications in Algebra.

Jeffrey Diller, Daniel Jackson, and Andrew J. Sommese, INVARIANT CURVES FOR BIRATIONAL SURFACE MAPS (PDF file, 18 pages), Transactions of the American Mathematical Society 359 (2007), 2973-2991.

Hidetoshi Maeda and Andrew J. Sommese, NOTES ON VERY AMPLE VECTOR BUNDLES ON 3-FOLDS (DVI file, 21 pages); postscript version; pdf version, Archiv der Mathematik, 85 (2005), 527-537.

Thomas Peternell and Andrew J. Sommese, AMPLE VECTOR BUNDLES AND BRANCHED COVERINGS, II (DVI file, 21 pages); postscript version; pdf version, Proceedings of the 2002 Fano Conference, Torino, edited by A. Collino, A. Conte, and M. Marchisio, (2004), 625-645.

Hidetoshi Maeda and Andrew J. Sommese, VERY AMPLE VECTOR BUNDLES OF CURVE GENUS TWO, Archiv der Math. 79 (2002), 74-80.

Mauro Beltrametti, Karen Chandler, and Andrew J. Sommese, REDUCIBLE HYPERPLANE SECTIONS II (2001) (DVI file, 12 pages); postscript version; pdf version, Kodai Math. J. 25 (2002), 139-150.

Antonio Lanteri and Andrew J. Sommese, AMPLE VECTOR BUNDLES WITH ZERO LOCI HAVING A HYPERELLIPTIC CURVE SECTION (2001); pdf version, Forum Mathematicum 15 (2003), 525-542.

Antonio Lanteri, Marino Palleschi, and Andrew J. Sommese, ON THE ADJUNCTION MAPPING OF VERY AMPLE VECTOR BUNDLES OF CORANK ONE (2001) (DVI file, 22 pages); postscript version; pdf version, Transactions of the American Mathematical Society 356 (2004), 2307-2324. Soc.

Mauro Beltrametti and Andrew J. Sommese, PROJECTIVE MANIFOLDS WITH SMALL PLURIDEGREES, Transactions of the American Mathematical Society 352 (2000) 3045-3064.

Sandra Di Rocco and Andrew J. Sommese, CHERN NUMBERS OF AMPLE VECTOR BUNDLES ON TORIC SURFACES (1999) (pdf version, 13 pages), Transactions of the American Mathematical Society 356 (2004), 587-598.

Thomas Peternell and Andrew J. Sommese, AMPLE VECTOR BUNDLES AND BRANCHED COVERINGS (with an appendix by Robert Lazarsfeld) (DVI file, 28 pages); postscript version; pdf version; Communications in Algebra 28 (2000), 5573-5599.

Stefan Kebekus, Thomas Peternell, Andrew J. Sommese, and Jaroslaw A. Wisniewski, PROJECTIVE CONTACT MANIFOLDS, Inventiones Mathematicae 142 (2000), 1-15.

Antonio Lanteri, Marino Palleschi, and Andrew J. Sommese, DISCRIMINANT LOCI OF VARIETIES WITH SMOOTH NORMALIZATION, (DVI file, 22 pages); postscript version; pdf version; Communications in Algebra 28 (2000), 4179-4200

Sandra Di Rocco and Andrew J. Sommese, LINE BUNDLES FOR WHICH A PROJECTIVIZED JET BUNDLE IS A PRODUCT, Proceedings of the Amer. Math. Soc. 129 (2001), 1659-1663.

Mauro Beltrametti, Sandra Di Rocco, and Andrew J. Sommese, ON GENERATION OF JETS FOR VECTOR BUNDLES, (DVI file, 14 pages); postscript version; pdf version; Revista Matematica Complutense 12 (1999) 27-45

Mauro Beltrametti, Alan Howard, Michael Schneider, and Andrew J. Sommese, PROJECTIONS FROM SUBVARIETIES, (DVI file, 27 pages); postscript version; pdf version; in ``Complex Analysis and Algebraic Geometry, Bayreuth, June 1998,'' edited by T. Peternell and F.O. Schreyer, (2000), 71-108, Walter de Gruyter, Berlin

Thomas Peternell, Michael Schneider, and Andrew J. Sommese, KODAIRA DIMENSION OF SUBVARIETIES, (DVI file, 16 pages); postscript version; pdf version; International Journal of Mathematics 10 (1999), 1065-1079.

Mauro Beltrametti and Andrew J. Sommese, PROJECTIVE MANIFOLDS WITH SMALL PLURIDEGREES, Trans. Amer. Math. Soc. 352 (2000), 3045-3064.

Karen Chandler, Alan Howard, and Andrew J. Sommese, REDUCIBLE HYPERPLANE SECTIONS I, (DVI file, 24 pages); postscript version; pdf version; Jour. Math. Soc. of Japan 51 (1999), 887-910.

Andrew J. Sommese, WHAT WE KNOW ABOUT THE SECOND ADJUNCTION MAPPING (1997), (DVI file, 26 pages); postscript version; pdf version; Rendiconti del Seminario Matematico e Fisico di Milano 67 (1997), 49-75 (2000)

Mauro Beltrametti and Andrew J. Sommese, ON THE DEGREE AND THE BIRATIONALITY OF THE SECOND ADJUNCTION MAPPING, (DVI file, 14 pages); postscript version; pdf version; Int. Jour. of Math. 10 (1999), 707-719.

Mauro Beltrametti and Andrew J. Sommese, SHARP MATSUSAKA-TYPE THEOREMS ON SURFACES, (DVI file, 12 pages); postscript version; pdf version; Math. Nachr. 191 (1998), 5-17.

Mauro Beltrametti and Andrew J. Sommese, ON THE SECOND ADJUNCTION MAPPING AND THE VERY AMPLENESS OF THE TRIADJOINT BUNDLE, (DVI file, 35 pages); postscript version; pdf version; In ``Birational Algebraic Geometry,'' edited by Y. Kawamata and V. Shokurov, Contemporary Mathematics 207 (1997), 1-24, American Mathematical Society, Providence, Rhode Island.

Antonio Lanteri, Hidetoshi Maeda, and Andrew J. Sommese, AMPLE AND SPANNED VECTOR BUNDLES OF MINIMAL CURVE GENUS, (DVI file, 11 pages); postscript version; pdf version; Archiv der Math. 66 (1996), 141-149.

Meeyoung Kim and Andrew J. Sommese, TWO RESULTS ON BRANCHED COVERINGS OF GRASSMANNIANS, (DVI file, 5 pages); postscript version; pdf version; J. Math. Kyoto Univ. 38 (1998), 21-27.

Mauro Beltrametti, Sandra Di Rocco, and Andrew J. Sommese, ON HIGHER ORDER EMBEDDINGS OF FANO THREEFOLDS BY THE ANTICANONICAL LINEAR SYSTEM, (DVI file, 15 pages); postscript version; pdf version; J. Math. Sci. University\ Tokyo 5 (1998), 75-97.

Mauro Beltrametti and Andrew J. Sommese, ON THE SECOND ADJUNCTION MAPPING. THE CASE OF A 1-DIMENSIONAL IMAGE, Trans. Amer. Math. Soc. 349 (1997), 3277-3302.

Mauro Beltrametti, Michael Schneider, and Andrew J. Sommese, CHERN INEQUALITIES AND SPANNEDNESS OF THE ADJOINT BUNDLE, postscript version; pdf version;in Proceedings of the Hirzebruch 65 conference at Bar-Ilan University , ed. by M. Teicher, Israel Mathematical Conf. Proc. 9 (1996), 97-107, American Mathematical Society, Providence, Rhode Island. (DVI file, 14 pages).

Mauro Beltrametti and Andrew J. Sommese, NOTES ON EMBEDDINGS OF BLOWUPS, Journal of Algebra, 186 (1996), 861-871.

Last updated July 30, 2007.