TY - GEN

T1 - Equations defining secant varieties

T2 - Abel Symposium 2009: Combinatorial Aspects of Commutative Algebra and Algebraic Geometry

AU - Sidman, Jessica

AU - Vermeire, Peter

PY - 2011

Y1 - 2011

N2 - In the 1980's, work of Green and Lazarsfeld (Invent. Math., 83, 1 (1985), 73-90; Compositio Math., 67, 3 (1988), 301-314), helped to uncover the beautiful interplay between the geometry of the embedding of a curve and the syzygies of its defining equations. Similar results hold for the first secant variety of a curve, and there is a natural conjectural picture extending to higher secant varieties as well. We present an introduction to the algebra and geometry used in (Sidman and Vermeire, Algebra Number Theory, 3, 4 (2009), 445-465) to study syzygies of secant varieties of curves with an emphasis on examples of explicit computations and elementary cases that illustrate the geometric principles at work.

AB - In the 1980's, work of Green and Lazarsfeld (Invent. Math., 83, 1 (1985), 73-90; Compositio Math., 67, 3 (1988), 301-314), helped to uncover the beautiful interplay between the geometry of the embedding of a curve and the syzygies of its defining equations. Similar results hold for the first secant variety of a curve, and there is a natural conjectural picture extending to higher secant varieties as well. We present an introduction to the algebra and geometry used in (Sidman and Vermeire, Algebra Number Theory, 3, 4 (2009), 445-465) to study syzygies of secant varieties of curves with an emphasis on examples of explicit computations and elementary cases that illustrate the geometric principles at work.

UR - http://www.scopus.com/inward/record.url?scp=84883650688&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-19492-4_9

DO - 10.1007/978-3-642-19492-4_9

M3 - Conference contribution

AN - SCOPUS:84883650688

SN - 9783642194917

T3 - Combinatorial Aspects of Commutative Algebra and Algebraic Geometry: The Abel Symposium 2009

SP - 155

EP - 174

BT - Combinatorial Aspects of Commutative Algebra and Algebraic Geometry

Y2 - 1 June 2009 through 4 June 2009

ER -