Brill–Noether divisors for even genus

Linear series on a curve of compact type bridged by a chain of elliptic curves

“…r−j(2,m 2 ) (q) − 2⌈ ν 2r ν 2r +1 ⌉, which gives the result (2). Thus the proof of the lemma is completed.…”

“…Our result combined with Theorem 1.1 [10] gives rise to some relations among Brill-Noether loci corresponding to ρ = −1, −2 in the moduli space M g . In particular, it will be shown that Brill-Noether loci of codimension two have mutually distinct supports in M g as in the case of Brill-Noether divisors [1,2].…”

“…Relationships among Brill-Noether divisors inside M g are useful for dealing with the birational geometry of M g [5,7,8]. It was known that any two Brill-Noether divisors have mutually distinct supports in M g [1,2]. On the one hand, every component of M r g,d has codimension at most −ρ(g, r, d) in M g ; further, in case −3 ≤ ρ(g, r, d) ≤ −1, each component of M r g,d is of codimension −ρ(g, r, d) [3,6,11].…”