caa a22 4500 445836148 CHVBK 20180317145330.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00209-009-0635-3 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0635-3 Cotterill Ethan Department of Mathematics and Statistics, Queen's University, K7L 3N6, Kingston, ON, Canada aut Geometry of curves with exceptional secant planes: linear series along the general curve [Elektronische Daten] [Ethan Cotterill] We study linear series on a general curve of genus g, whose images are exceptional with regard to their secant planes. Working in the framework of an extension of Brill-Noether theory to pairs of linear series, we prove that a general curve has no linear series with exceptional secant planes, in a very precise sense, whenever the total number of series is finite. Next, we partially solve the problem of computing the number of linear series with exceptional secant planes in a one-parameter family in terms of tautological classes associated with the family, by evaluating our hypothetical formula along judiciously-chosen test families. As an application, we compute the number of linear series with exceptional secant planes on a general curve equipped with a one-dimensional family of linear series. We pay special attention to the extremal case of d-secant (d − 2)-planes to (2d − 1)-dimensional series, which appears in the study of Hilbert schemes of points on surfaces. In that case, our formula may be rewritten in terms of hypergeometric series, which allows us both to prove that it is nonzero and to deduce its asymptotics in d. Springer-Verlag, 2009 Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 549-582 0025-5874 267:3-4<549 2011 267 209 https://doi.org/10.1007/s00209-009-0635-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0635-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Cotterill Ethan Department of Mathematics and Statistics, Queen's University, K7L 3N6, Kingston, ON, Canada aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 549-582 0025-5874 267:3-4<549 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer