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Bernd Sturmfels
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21	Math 255: Algebraic Curves Bernd Sturmfels, UC Berkeley, Fall 2011 Homework # 3, due Tuesday, September[removed]Kirwan 4.5] Prove: Every cuspidal cubic curve in the plane P2 is projectively equivalent to the curve {y 2 z Add to Reading List Source URL: math.berkeley.edu Language: English - Date: 2011-09-04 09:19:14 Differential geometry Cubic plane curve Dual curve Riemann surface Geometry Algebraic geometry Algebraic curves
22 $Math 255: Algebraic Curves Bernd Sturmfels, UC Berkeley, Fall 2011 Homework # 5, due Tuesday, November[removed]Fulton[removed]Fix a DVR R with quotient field K and maximal ideal m. (a) Show that if z ∈ K\R then z −1 ∈$	Math 255: Algebraic Curves Bernd Sturmfels, UC Berkeley, Fall 2011 Homework # 5, due Tuesday, November[removed]Fulton[removed]Fix a DVR R with quotient field K and maximal ideal m. (a) Show that if z ∈ K\R then z −1 ∈ Add to Reading List Source URL: math.berkeley.edu Language: English - Date: 2011-10-13 10:43:57 Algebraic curves Linear system of divisors Divisor Curve Quartic plane curve Intersection number Local parameter Algebraic geometry Abstract algebra Geometry
23	Math 255: Algebraic Curves Bernd Sturmfels, UC Berkeley, Fall 2011 Homework # 4, due Tuesday, October[removed]Let c denote the circumference of the ellipse defined by 2x2 + 3y 2 = 5. ComputeR c numerically up to 15 digits Add to Reading List Source URL: math.berkeley.edu Language: English - Date: 2011-09-12 09:46:52 Algebraic varieties Vector bundles Canonical bundle Algebraic curves Holomorphic function Divisor Riemann surface Meromorphic function Differentiable manifold Algebraic geometry Geometry Abstract algebra
24	Math 255: Algebraic Curves Bernd Sturmfels, UC Berkeley, Fall 2011 Homework # 1, due Thursday, September[removed]Kirwan 2.2] Find the singular points, and the tangent lines at the singular points, of each of the following Add to Reading List Source URL: math.berkeley.edu Language: English - Date: 2011-05-29 17:17:59 Elliptic curves Projective geometry Algebraic geometry Algebraic curve Algebraic variety Curve Elliptic curve Projective space Geometry Abstract algebra Elliptic curve cryptography
25	Likelihood Geometry June Huh and Bernd Sturmfels Abstract We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a Add to Reading List Source URL: web.math.unifi.it Language: English - Date: 2013-06-02 06:13:51 Projective space Divisor Curve Algebraic curve Maximum likelihood Projective geometry Algebraic variety Riemann surface Ample line bundle Geometry Abstract algebra Algebraic geometry
26	Ruriko Yoshida Department of Statistics University of Kentucky 325D Multidisplinary Science Building Lexington KY[removed][removed] Add to Reading List Source URL: www.polytopes.net Language: English - Date: 2014-05-07 06:43:13 Applied mathematics Algebraic statistics Algebraic geometry Integer points in convex polyhedra Mathematical and theoretical biology Computer algebra system Combinatorics Discrete mathematics Algebraic biology Mathematics Academia Bernd Sturmfels
27	Teaching the Geometry of Schemes Gregory G. Smith and Bernd Sturmfels This chapter presents a collection of graduate level problems in algebraic geometry illustrating the power of Macaulay 2 as an educational tool. When Add to Reading List Source URL: www.math.uiuc.edu Language: English - Date: 2001-05-18 17:20:58 Prime ideals Commutative algebra Algebraic number field Algebraic number theory Field theory Ring Algebraic geometry Ideal Spectrum of a ring Abstract algebra Algebra Algebraic structures
28	Ideals, Varieties and Macaulay 2 Bernd Sturmfels? This chapter introduces Macaulay 2 commands for some elementary computations in algebraic geometry. Familiarity with Gr¨ obner bases is assumed. Many students and resear Add to Reading List Source URL: www.math.uiuc.edu Language: English - Date: 2001-04-28 11:06:43 Commutative algebra Polynomials Algebraic structures Algebraic geometry Monomial order Ideal Monomial Polynomial ring Polynomial Abstract algebra Algebra Ring theory
29	ACM 8 http://www.springer.de Add to Reading List Source URL: www.math.uiuc.edu Language: English - Date: 2002-01-07 18:01:22 Macaulay2 Macaulay computer algebra system David Eisenbud Bernd Sturmfels Algebraic geometry Commutative algebra Francis Sowerby Macaulay Combinatorial commutative algebra Mathematics Algebra Academia
30	Algorithms for the Toric Hilbert Scheme Michael Stillman, Bernd Sturmfels, and Rekha Thomas The toric Hilbert scheme parametrizes all algebras isomorphic to a given semigroup algebra as a multigraded vector space. All co Add to Reading List Source URL: www.math.uiuc.edu Language: English - Date: 2001-04-28 11:06:30 Commutative algebra Algebraic structures Ring theory Invariant theory Polynomials Hilbert series and Hilbert polynomial Monomial Ideal Algebraic geometry Abstract algebra Algebra Mathematics