Progress on Syzygies of Algebraic Curves
نویسنده
چکیده
These notes discuss recent advances on syzygies on algebraic curves, especially concerning the Green, the Prym-Green and the Green-Lazarsfeld Secant Conjectures. The methods used are largely geometric and variational, with a special emphasis on examples and explicit calculations. The notes are based on series of lectures given in Daejeon (March 2013), Rome (November-December 2015) and Guanajuato (February 2016).
منابع مشابه
Three Themes of Syzygies
We present three exciting themes of syzygies, where major progress has been made recently: Boij-Söderberg theory, Stillman’s question, and syzygies over complete intersections. Free resolutions are both central objects and fruitful tools in commutative algebra. They have many applications in algebraic geometry, computational algebra, invariant theory, hyperplane arrangements, mathematical physi...
متن کاملNew evidence for Green’s conjecture on syzygies of canonical curves
Some twelve years ago, Mark Green [G] made a few conjectures regarding the behaviour of syzygies of a curve C imbedded in IP n by a complete linear system. The so-called generic Green conjecture on canonical curves pertains to this question when the linear system is the canonical one and the curve is generic in the moduli, and predicts what are the numbers of syzygies in that case. Green and La...
متن کاملSyzygies of Curves beyond Green’s Conjecture
We survey three results on syzygies of curves beyond Green’s conjecture, with a particular emphasis on drawing connections between the study of syzygies and other topics in moduli theory.
متن کاملLectures on the Geometry of Syzygies
The theory of syzygies connects the qualitative study of algebraic varieties and commutative rings with the study of their defining equations. It started with Hilbert’s work on what we now call the Hilbert function and polynomial, and is important in our day in many new ways, from the high abstractions of derived equivalences to the explicit computations made possible by Gröbner bases. These le...
متن کاملGeometric Invariant Theory of Syzygies, with Applications to Moduli Spaces
We define syzygy points of projective schemes, and introduce a program of studying their GIT stability. Then we describe two cases where we have managed to make some progress in this program, that of polarized K3 surfaces of odd genus, and of genus six canonical curves. Applications of our results include effectivity statements for divisor classes on the moduli space of odd genus K3 surfaces, a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017