The search interface is made of three sections: Search, Explore, and Results. These are described in detail below.
You may start searching either from the Search section or from the Explore section.
Search
This section shows your current search criteria and allows you to submit keywords to search in the bibliography.
Each new submission adds the entered keywords to the list of search criteria.
To start a new search instead of adding keywords to the current search, use the Reset search button, then enter your new keywords.
To replace an already submitted keyword, first remove it by unchecking its checkbox, then submit a new keyword.
You may control the extent of your search by selecting where to search. The options are:
Everywhere: Search your keywords in all bibliographic record fields and in the text content of the available documents.
In authors or contributors: Search your keywords in author or contributor names.
In titles: Search your keywords in titles.
In publication years: Search a specific publication year (you may use the OR operator with your keywords to find records having different publication years, e.g., 2020 OR 2021).
In all fields: Search your keywords in all bibliographic record fields.
In documents: Search your keywords in the text content of the available documents.
You may use boolean operators with your keywords. For instance:
AND: Finds entries that contain all specified terms. This is the default relation between terms when no operator is specified, e.g., a b is the same as a AND b.
OR: Finds entries that contain any of the specified terms, e.g., a OR b.
NOT: Excludes entries that contain the specified terms, e.g., NOT a.
Boolean operators must be entered in UPPERCASE.
You may use logical groupings (with parentheses) to eliminate ambiguities when using multiple boolean operators, e.g., (a OR b) AND c.
You may require exact sequences of words (with double quotes), e.g., "a b c". The default difference between word positions is 1, meaning that an entry will match if it contains the words next to each other, but a different maximum distance may be specified (with the tilde character), e.g., "web search"~2 allows up to 1 word between web and search, meaning it could match web site search as well as web search.
You may specify that some words are more important than others (with the caret), e.g., faceted^2 search browsing^0.5 specifies that faceted is twice as important as search when computing the relevance score of the results, while browsing is half as important. Such term boosting may be applied to a logical grouping, e.g., (a b)^3 c.
Keyword search is case-insentitive, accents are folded, and punctuation is ignored.
Stemming is performed on terms from most text fields, e.g., title, abstract, notes. Words are thus reduced to their root form, saving you from having to specify all variants of a word when searching, e.g., terms such as search, searches, and searching all produce the same results. Stemming is not applied to text in name fields, e.g., authors/contributors, publisher, publication.
Explore
This section allows you to explore categories associated with the references.
Categories can be used to filter your search. Check a category to add it to your search criteria and narrow your search. Your search results will then only show entries that are associated with that category.
Uncheck a category to remove it from your search criteria and broaden your search results.
The numbers shown next to the categories indicate how many entries are associated with each category in the current set of results. Those numbers will vary based on your search criteria to always describe the current set of results. Likewise, categories and whole facets will disappear when the result set has no entry associated to them.
An arrow icon () appearing next to a category indicates that subcategories are available. You may press it to expand a list of more specific categories. You may press it again later to collapse the list. Expanding or collapsing subcategories will not change your current search; this allows you to quickly explore a hierarchy of categories if desired.
Results
This section shows the search results. When no search criteria has been given, it shows the full content of the bibliography (up to 20 entries per page).
Each entry of the results list is a link to its full bibliographic record. From the bibliographic record view, you may continue exploring the search results by going to previous or following records in your search results, or you may return to the list of results.
Additional links, such as Read document or View on [website name], may appear under a result. These give you quick access to the resource. Those links will also be available in the full bibliographic record.
The Abstracts button lets you toggle the display of abstracts within the list of search results. Enabling abstracts, however, will have no effect on results for which no abstract is available.
Various options are provided to let you sort the search results. One of them is the Relevance option, which ranks the results from most relevant to least relevant. The score used for ranking takes into account word frequencies as well as the fields where they appear. For instance, if a search term occurs frequently in an entry or is one of very few terms used in that entry, that entry will probably rank higher than another where the search term occurs less frequently or where lots of other words also occur. Likewise, a search term will have more effect on the scores if it is rare in the whole bibliography than if it is very common. Also, if a search term appears in, e.g., the title of an entry, it will have more effect on the score of that entry than if it appeared in a less important field such as the abstract.
The Relevance sort is only available after keywords have been submitted using the Search section.
Categories selected in the Explore section have no effect on the relevance score. Their only effect is to filter the list of results.
Let X and Y be varieties over a field k; π : X → Y is a quadruple cover of Y if π*script O signX is a locally free, rank 4 script O signY-algebra. If char k ≠ 2, we see that π*script O signX splits as script O signY ⊕ε where ε is a locally free rank 3 sheaf over script O signY, which is locally the "trace zero" module. For each y ∈ Y, we therefore have a rank 4 associative, commutative algebra over script O signY,y. We find that these algebras are parametrized by an affine cone over the Grassmanian G(2, 6) with vertex corresponding to the algebra k[x, y, z]/(x, y, z)2. We then show that a quadruple cover with trace zero module ε over a variety Y is determined by a totally decomposable section η ∈ H0(∧2S2 E* ⊗ ∧3 E). We then examine the case in which the section η has no zeros. Here, each rank 4 algebra may be associated to a pencil of conics. As a special case of this, we look at the work of G. Casnati and T. Ekedahl on Gorenstein covers, and we show that their analysis is the subcase where the pencil of conics has length 4 base locus. Finally, we study the case in which the trace zero module ε is split. In this context, Galois covers, which are covers induced by the action of a group of order 4 on the covering variety X, are also studied.