ABSTRACT. Corresponding to a morphism /: V -* W of algebraic varieties (such that dim(K) < dim(lV)), we construct a family of subschemes S^)(/) C V. When V and W are nonsingular, the s[^\ q > 1, induce a filtration of the set of closed points x S V such that the tangent space map dfx: T(V)X -T(W)f,xs has rank = dim(10 -1. We prove that if V is a 0. Introduction. Let k be an algebraically closed field, and let V be a nonsingular projective variety over k. As in [11], we consider an embedding PCP" (projective «-space) and a finite morphism 7r: V -*■ Pm, where dim(P) < m < 2 • dim(P), induced by projection from an (« -m -l)-subspace LCP". We study certain properties of generic projections, i.e. properties which 77 has when L corresponds to a point of a suitable dense open subset of the Grassmann variety G(n, n -m -1).When m > dim(P), one objective is to describe the structure of the local rings Oy'¡y, where y EV = 77(F) C Pm. (If (A, m) is a local ring, then 4 is its completion in the m-adic topology.) Using our main results, which are stated in § 1, this can be done in the case that the map of Zariski tangent spaces dux : Tv x -► Tfm has rank > dim(P) -1 for all x G tt-1^). Detaüs of this are given in §13. If m = dim(P), the corresponding problem is to describe the local structure of the branch locus 7r(Sj (tt)) C Pm. (Sj (tt) is defined in §2.) I have obtained some results concerning this problem which wül appear in another paper. (See also [14].) The results of the present paper were announced in [13]. I would

In reaction to evolution in the way information is digested, libraries have undergone a transformation over the past couple of decades. Consequently, libraries everywhere have become more than just warehouses for books. Being a relatively new field, arts entrepreneurship has the opportunity to continue to grow along with libraries. This essay discusses ways that academic libraries can benefit arts entrepreneurship educators, as well as possibilities for collaboration between the two areas for research and planning events. Reaching out and establishing relationships with library personnel serves to reinforce the foundation of any arts entrepreneurship program.

Context One of the two major pathways to become a physician in the United States is the Doctor of Osteopathic Medicine (DO) degree. A major distinctive feature is often perceived as the addition of manual training in osteopathic manipulative treatment (OMT) in the DO education. However, the profession also has a distinct philosophy imbedded in the curriculum of all osteopathic medical schools. Many medical schools offer professional degrees with graduates who may choose to continue their education in medicine, such as the Master of Science in Biomedical Sciences (MSBS). At our institution, there is no formal exposure to the differences between osteopathic and allopathic medicine in the MSBS curriculum, and most of this understanding is gained through out-of-classroom conversations. During the SARS-CoV-2 pandemic, virtual learning prohibited the usual gathering and discourse that occurs when students are learning on campus. Objectives The objective of this study is to create a curriculum in the form of a seminar series to assist premedical students in making an informed choice about which profession is the best fit for their own education and to gain an appreciation for osteopathic medicine. This appreciation could also aid in the future collaboration of premedical students with osteopathic providers, recommendations to patients, and potentially their own medical care. Questionnaires were utilized to determine if our osteopathic seminar series was effective at changing the preferences and understanding of MSBS students. We also sought to determine the effectiveness of virtual vs. in-person delivery of our curriculum. Methods A seminar series with pre-established objectives was developed and presented to MSBS students at an osteopathic institution during the Fall of 2020 and 2021. The 2020 seminar was delivered through a virtual conference platform, and the 2021 seminar was delivered in-person. An eight question pre-and postquestionnaire was given to participants to evaluate their preferences and understanding. Internal validity and differences between delivery formats were assessed. Results Both seminar series produced equally effective, significant changes in the preferences and perceptions of osteopathic medicine in both virtual and in-person delivery formats. Differences in pre-vs. post understanding across both seminar series were not consistently significant and were smaller than those observed in preferences and perceptions. Positive changes included an increased willingness to see a DO and to recommend a loved one see a DO as their personal physician. Preference changes between the in-person vs. virtual delivery platforms did not show significant differences; however, understanding did show some inconsistent differences. Conclusions This study demonstrates the utility of a virtual or in-person seminar to improve the preferences and perceptions of the osteopathic profession in MSBS students. The seminar series was successful in its goal of offering formal exposure to the osteopathic profession. The improved preferences and perceptions will have potential substantial benefits to the field of osteopathic medicine in the future. Further research is warranted to determine the most effective way to increase understanding of the osteopathic profession.

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