## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Friday, November 27, 2020 — 2:30 PM EST

**Brady Ali Medina, Department of Pure Mathematics, University of Waterloo**

"A different way to generalize the Weierstrass semigroup"

We propose a different way to generalize the concept of a Weierstrass semigroup H_P associated to a point P in a curve X of genus g. We start by defining the Weierstrass set of a vector bundle F with respect to a point P, and we prove that this set is an H_P - relative ideal. Also, if the vector bundle is semistable, we prove that the largest gap is less than 2g − μ(F), where μ(F) denotes the slope of F. Furthermore, when F is a line bundle, we define the Weierstrass semigroup of F with respect to a divisor D and we find that the largest gap is less than 2g − deg(F)/ deg(D). Moreover, in the case when D = P we find that the cardinality of the set of gaps is exactly l(K_X − deg(F)), which is a theorem analogous to the Weierstrass Gap Theorem.

Zoom meeting: https://zoom.us/j/93859138328

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.