Minimal Free Resolutions of Paracanonical Curves of Odd Genus
نویسنده
چکیده
We prove the Prym–Green conjecture on minimal free resolutions of paracanonical curves in the case where the genus is odd.
منابع مشابه
The Resolution of Paracanonical Curves of Odd Genus
We prove the Prym–Green conjecture on minimal free resolutions of paracanonical curves of odd genus. The proof proceeds via curves lying on ruled surfaces over an elliptic curve.
متن کاملThe Prym–green Conjecture for Torsion Line Bundles of High Order
Using a construction of Barth and Verra that realizes torsion bundles on sections of special K3 surfaces, we prove that the minimal resolution of a general paracanonical curve C of odd genus g and order ` ≥ √ g+2 2 is natural, thus proving the Prym–Green Conjecture of [CEFS] . In the process, we confirm the expectation of Barth–Verra concerning the number of curves with `-torsion line bundle in...
متن کاملRibbons and Their Canonical Embeddings
We study double structures on the projective line and on certain other varieties, with a view to having a nice family of degenerations of curves and K3 surfaces of given genus and Cli ord index. Our main interest is in the canonical embeddings of these objects, with a view toward Green's Conjecture on the free resolutions of canonical curves. We give the canonical embeddings explicitly, and exh...
متن کاملSyzygies, finite length modules, and random curves
We apply the theory of Gröbner bases to the computation of free resolutions over a polynomial ring, the defining equations of a canonically embedded curve, and the unirationality of the moduli space of curves of a fixed genus.
متن کاملMap of Degree 2
We classify the minimal algebraic surfaces of general type with pg = q = 1, K 2 = 8 and bicanonical map of degree 2. It will turn out that they are isogenous to a product of curves, so that if S is such a surface then there exist two smooth curves C, F and a finite group G acting freely on C × F such that S = (C × F)/G. We describe the C, F and G that occur. In particular the curve C is a hyper...
متن کامل