Variety of Singular Quadrics Containing a Projective Curve
\.Irfan Kad{\i}k\"oyl\"u

TL;DR
This paper investigates the geometry of quadrics containing a general projective curve, constructs new divisor classes in moduli spaces, and proves that ar{al M}_{15,9} is of general type.
Contribution
It introduces new divisor classes in moduli spaces via the study of quadrics containing curves, and establishes the general type of ar{al M}_{15,9}.
Findings
Variety of quadrics has expected dimension in certain ranges.
Constructed new divisor classes in ar{al M}_{g,n}.
Proved ar{al M}_{15,9} is of general type.
Abstract
We study the variety of rank quadrics containing a general projective curve and show that it has the expected dimension in the range . By considering the loci where this expectation is not true, we construct new divisor classes in . We use one of these classes to show that is of general type.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Coding theory and cryptography · Cryptography and Residue Arithmetic
